This study has 2 phases: Phase 1 (dose escalation) and Phase 2 (dose expansion).

The goal of Phase 1 of this clinical research study is to find the highest tolerable dose combination of selumetinib and olaparib that can be given to patients who have solid tumors that are advanced or recurrent (has returned after treatment).

The goal of Phase 2 is to learn if the highest tolerable dose combination found in Phase 1 can help to control advanced or recurrent solid tumors.

The safety of the study drug combination will also be studied in both parts.

This is an investigational study. Selumetinib is not FDA approved or commercially available. It is currently being used for research purposes only. Olaparib is FDA approved and commercially available for the treatment of ovarian cancer that has a certain type of genetic mutation (change). It is considered investigational to use selumetinib in combination with olaparib to treat advanced or recurrent cancer.

The study doctor can explain how the study drugs are designed to work. Up to 90 participants will be enrolled in this study. All will take part at MD Anderson.

Study Groups:

If you are found to be eligible to take part in this study, you will be assigned to a phase depending on when you join the study. Up to 30 participants will be enrolled in Phase 1, and up to 60 participants will be enrolled in Phase 2.

If you are enrolled in Phase 1, the dose of the study drugs you receive will depend on when you join this study. Up to 3 dose level combinations of selumetinib and olaparib will be tested. The first group of participants will receive the lowest dose level of each study drugs. Each new group will receive a higher dose of either selumetinib or olaparib study drugs than the group before it, if no intolerable side effects were seen. This will continue until the highest tolerable dose combination of the study drugs is found.

If you are enrolled in Phase 2, you will receive the highest study drug combination that was tolerated in Phase 1.

Study Drug Administration:

Each study cycle is 28 days.

You will take both selumetinib and olaparib by mouth 2 times each day, about 12 hours apart (1 dose in the morning, 1 dose in the evening). You should fast (have nothing to eat or drink except water) for at least 2 hours before and 1 hour after your dose. If you vomit or miss a dose, you should not retake the dose. Wait and take your next scheduled dose.

Depending on the dose level of selumetinib you are receiving, you may only take the study drug on Days 1-5 of each week. The study doctor will tell you how often you should take selumetinib.

You will be given a study drug diary to record when you take each dose. The study staff will show you how to fill it out.

You will wait to take your morning dose of study drugs at the clinic on certain days. The study staff will remind you before each of these clinic visits.

Length of Treatment:

You may continue to receive the study drugs for as long as the study doctor thinks it is in your best interest. You will no longer be able to receive the study drugs if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions.

Your active participation on the study will be over after the 30-day follow-up visit; however, you will be contacted by phone every 3 months to check on you and the status of the disease.

Study Visits:

On Days 1 and 15 of Cycle 1:

• You will have a physical exam
• Blood (about 3 tablespoons) will be drawn for routine and PD testing.
• If you are in Phase 1, part of this sample on Day 1 will be used for pharmacokinetic (PK) testing. PK testing measures the amount of study drug in the body at different time points.
• If you are in Phase 2, part of this sample will be used for tumor marker testing.
• You will have an EKG.
• On Day 15, if you are in Phase 2, you will have a tumor biopsy for PD testing, including genetic testing.

On Day 8 of Cycle 1:

• You will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine and PD tests. If you are in Phase 2, part of this sample will be used for tumor marker testing.
• You will have an EKG.

On Day 22 of Cycle 1:

• You will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine and PD tests. If you are in Phase 2 and have endometrial or ovarian cancer, part of this blood will be used for tumor marker testing.

On Day 1 of Cycle 2:

• You will have a physical exam.
• You will have an eye exam.
• Blood (about 3 tablespoons) will be drawn for routine and PD tests.
• If you are in Phase 1, part of this blood will be used for PK testing.
• If you are in Phase 2, part of this blood will be used for tumor marker testing.

On Day 26 of Cycle 2, you will have an MRI or a CT scan.

On Day 1 of Cycles 3 and beyond:

• You will have a physical exam
• Blood (about 3 tablespoons) will be drawn for routine and PD tests. If you are in Phase 2, part of this blood will be used for tumor marker testing.

Starting on Day 1 of Cycle 4 and every 3 cycles after that, you will have an ECHO.

During Cycles 4 and 6 and then every 3 cycles after that (Cycles 9, 12, 15, and so on), you will have MRI or a CT scan.

At any time the study doctor thinks it is needed, you may have some or all of these tests repeated to check on your health.

End-of-Treatment Visit:

Within 7 days after your last dose of study drugs:

• You will have a physical exam.
• Blood (about 3 tablespoons) will be drawn for routine and PD tests.
• If it has been more than 28 days since the last scan, you will have an MRI or CT scan.

Follow-Up:

About 30 days after your last study drug dose:

• You will have a physical exam.
• Blood (about 2 tablespoons) will be drawn for routine tests.

You may be called by a member of the study staff every 3 months to ask how you are doing and if you have had any side effects. This call should last about 5-10 minutes.

Inclusion Criteria:

1. Written informed consent obtained from the subject prior to performing any protocol-related procedures, including screening evaluations.
2. Age >/= 18 years at time of study entry
3. Patients with advanced cancer that is refractory to standard therapy, or that has either relapsed after standard therapy or has no standard therapy that increases survival by at least three months.
4. Patients may have unlimited prior chemotherapy treatments.
5. For dose escalation phase, patients may have evaluable or measurable disease. For ovarian cancer, if no measurable disease is present, patients should have assessable disease such as pleural effusion, ascites, with CA-125 GCIG criteria.
6. For dose expansion phase, patients must have at least one site of measurable disease as defined by RECIST criteria (Version 1.1).
7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
8. All prior treatment-related toxicities must be Common Terminology Criteria for Adverse Events (CTCAE) (Version 4.03) </= Grade 1 at the time of screening (except alopecia).
9. Life expectancy of >/= 16 weeks.
10. Adequate normal organ and marrow function as defined by: Hemoglobin >/= 10.0 g/dL with no blood transfusion within 28 days of starting treatment; White blood cells (WBC) >3 x 10^9/L; Absolute neutrophil count (ANC) >/= 1.5 x 10^9/L (> 1500 per mm^3); Platelet count >/= 100 x 10^9/L (>100,000 per mm^3); Serum bilirubin </= 1.5 x institutional upper limit of normal (ULN); AST (SGOT) and ALT (SGPT) </= 2.5 x ULN unless liver metastases are present, in which case it must be </= 5x ULN; Serum creatinine CL>50 mL/min by the Cockcroft-Gault formula (Cockcroft and Gault 1976) or by 24-hour urine collection for determination of creatinine clearance--Creatinine CL (ml/min)=[Weight(kg)*(140-Age)*(0.85 for females or 1 for males)/[72*serum creatinine (mg/dL)].
11. Subject is willing and able to comply with the protocol for the duration of the study including undergoing treatment and scheduled visits and examinations including follow up.
12. Postmenopausal or evidence of non-childbearing status for women of childbearing potential: negative urine or serum pregnancy test within 7 days of study treatment. Postmenopausal is defined as: amenorrheic for 1 year or more following cessation of exogenous hormonal treatments; luteinizing hormone (LH) and follicle stimulating hormone (FSH) levels in the postmenopausal range for women under 50; radiation-induced oophorectomy with last menses > 1 year ago; chemotherapy-induced menopause with > 1 year interval since last menses; OR surgical sterilization (bilateral oophorectomy or hysterectomy).
13. Female patients of childbearing potential must use two highly effective forms of contraception.
14. Male patients must use a condom during treatment and for 3 months after the last dose of olaparib when having sexual intercourse with a pregnant woman or with a woman of childbearing potential. Female partners of male patients should also use a highly effective form of contraception if they are of childbearing potential.
15. Additional criteria for escalation cohorts: A) Patients must have RPA (including KRAS, NRAS, NF1, HRAS, and BRAF); B) Prior treatment with MEK inhibitors and/or PARP inhibitors is allowed.
16. Additional criteria for expansion cohorts: A) Patients must have histologically-confirmed advanced or recurrent ovarian cancer with RPA or that had progression during prior PARP inhibitor treatment, endometrial cancer with RPA, or other solid tumor types with RPA; B) Measurable and biopsy-accessible disease; C) Patient must be willing to undergo biopsy procedure; D) Prior treatment with PARP inhibitors is allowed.

Exclusion Criteria:

1. Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site).
2. Previous enrollment in the present study.
3. Participation in another clinical study with an investigational product during the 4 weeks prior to therapy initiation.
4. Recent major surgery within 4 weeks prior to starting study treatment. Minor surgery within 2 weeks of starting study treatment. Patients must be recovered from effects of surgery.
5. Patients receiving any systemic chemotherapy or radiotherapy (except for palliative reasons) within 3 weeks prior to study treatment initiation.
6. Concomitant use of known strong (e.g., phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's Wort) or moderate CYP3A inducers (e.g., bosentan, efavirenz, modafinil). The required washout period prior to starting olaparib is 5 weeks for enzalutamide or phenobarbital and 3 weeks for other agents.
7. Concomitant use of known strong CYP3A inhibitors (e.g., itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir) or moderate CYP3A inhibitors (e.g., ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil). The required washout period prior to starting olaparib is 2 weeks.
8. Concomitant use of other anti-cancer therapy (chemotherapy, immunotherapy, hormonal therapy (Hormone replacement therapy is acceptable), radiotherapy (except for palliative), biological therapy or other novel agent) or live virus and live bacterial vaccines while the patient is receiving study medication. Strong or Moderate CYP3A inhibitors and inducers should not be taken with study treatment; however, if no other suitable alternative concomitant medication is available, dose reductions may be allowed under careful monitoring.
9. Known severe hypersensitivity to selumetinib or olaparib, their comparators, or combination medications or any excipient of these medicinal products, or history of allergic reactions attributed to compounds of similar chemical or biologic composition to selumetinib or olaparib, or their comparator.
10. History of another primary malignancy except for: A) Malignancy treated with curative intent and with no known active disease >/= 3 years before the first dose of study drug and of low potential risk for recurrence; B) Adequately treated non-melanoma skin cancer or lentigo maligna without evidence of disease; C) Adequately treated carcinoma in situ without evidence of disease, e.g. cervical cancer in situ; D) Synchronous endometrial and ovarian cancer is allowed, provided the endometrial cancer is presumed Stage IA/B grade 1/2.
11. Any unresolved toxicity (>/= CTCAE grade 2) from previous anti-cancer therapy, excluding alopecia.
12. Known or suspected brain metastases or spinal cord compression, unless the condition has been asymptomatic, has been treated with surgery and/or radiation, and has been stable without requiring corticosteroids nor anticonvulsant medications for at least 4 weeks prior to the first dose of study medication. Patients with history of brain metastases should undergo brain imaging within 4 weeks of therapy initiation and at each restaging.
13. Known myelodysplastic syndrome/acute myeloid leukemia or with features suggestive of MDS/AML.
14. Female subjects who are pregnant/breast-feeding or who are of reproductive potential and not employing acceptable methods of birth control.
15. Cardiac conditions as follows: Uncontrolled hypertension (BP >/= 150/95 mmHg despite medical therapy); Acute coronary syndrome within 6 months prior to starting treatment; Uncontrolled Angina - Canadian Cardiovascular Society grade II-IV despite medical therapy; Symptomatic heart failure NYHA Class II-IV, prior or current cardiomyopathy, or severe valvular heart disease; Prior or current cardiomyopathy including but not limited to the following: known hypertrophic cardiomyopathy or known arrhythmogenic right ventricular cardiomyopathy; Previous moderate or severe impairment of left ventricular systolic function (LVEF <45% on echocardiography or equivalent on MUGA) even if full recovery has occurred; Severe valvular heart disease;
16. (Continued from previous) Baseline LVEF below the LLN measured by ECHO or institution's LLN for MUGA; Atrial fibrillation with a ventricular rate >100 bpm on ECG at rest; QTcF >470ms on two or more timepoints or other factors that increase the risk of QT prolongation such as family history of long QT syndrome.
17. Ophthalmological conditions as follows: Current or past history of retinal pigment epithelial detachment (RPED)/central serous retinopathy (CSR) or retinal vein occlusion; or Intraocular pressure (IOP) > 21 mmHg or uncontrolled glaucoma (irrespective of IOP)
18. Any evidence of a severe or uncontrolled systemic disease (e.g. unstable or uncompensated respiratory, cardiac, hepatic, or renal disease, active infection (including hepatitis B, hepatitis C, human immunodeficiency virus [HIV]), active bleeding diatheses or renal transplant.
19. Previous allogenic bone marrow transplant or double umbilical cord blood transplantation.
20. Whole blood transfusion in the last 120 days prior to entry to the study.
21. Patient is confirmed to have actively symptomatic pneumonitis.
22. Extensive bilateral lung disease on high-resolution computed tomography (HRCT) scan.
23. Patients unable to swallow orally administered medication and patients with gastrointestinal disorders likely to interfere with absorption of the study medication.
24. Immunocompromised patients, e.g. patients known to be serologically positive for HIV. Patients do NOT need to be tested for HIV in order to enroll on study.
25. Evidence of any other significant clinical disorder or laboratory finding that, in the opinion of the investigator, would interfere with evaluation of study treatment or interpretation of patient safety or study results.
26. For the expansion cohorts only: Prior treatment with any MEK inhibitor is not allowed in the expansion cohorts.](streamdown:incomplete-link)