To find the recommended dose of the drug paclitaxel that can be given intraperitoneally (given directly into the abdominal cavity) to participants with metastatic appendiceal adenocarcinoma.

Primary (Phase I):

1. To assess the maximum tolerated dose (MTD) of paclitaxel via IP route given every 14 days in subjects with metastatic appendiceal adenocarcinoma

   Primary (Phase II):

2. To assess the pathologic and radiographic objective response rate of paclitaxel via IP route in participants with metastatic appendiceal adenocarcinoma

Secondary Objectives

1. To assess the progression-free and overall survival of metastatic appendiceal adenocarcinoma treated with IP paclitaxel. Although the clinical benefit of this drug has not yet been established, the intent of offering this treatment is to provide a possible therapeutic benefit, and thus the participants will be carefully monitored for tumor response and symptom relief in addition to safety and tolerability
2. To assess the pharmacokinetics of IP PTX
3. To assess the change in PCI following IP PTX in patients with metastatic appendiceal adenocarcinoma
4. To assess rate of initially unresectable participants with metastatic appendiceal adenocarcinoma able to undergo CRS / HIPEC after IP PTX
5. To assess the rate of conversion from positive to negative cytology in peritoneal fluid following IP PTX in participants with metastatic appendiceal adenocarcinoma
6. To assess the prognostic value of circulating tumor DNA (ctDNA) in participants with metastatic appendiceal adenocarcinoma and the correlation of quantitative ctDNA measurement with radiographic and pathologic response
7. To generate PDX and PDO models of appendiceal adenocarcinoma and evaluate their ability to predict response of human tumors
8. To evaluate the effect of IP PTX on the transcriptomic state of appendiceal adenocarcinoma and the tumor microenvironment (TME) through comparison of pre- and post-treatment specimens
9. To assess the impact of GNAS, KRAS, TP53, and APC mutation on response to IP PTX therapy
10. To assess the impact of mucinous, signet ring cell, and goblet cell histology on response to IP PTX therapy

Inclusion Criteria:

1. Age 18 years and above. There will be no upper age restriction

2. ECOG performance status ≤ 2

3. Participants must have histologically confirmed diagnosis of unresectable locally metastatic appendiceal adenocarcinoma

4. Metastatic disease in the peritoneal cavity and not a candidate for cytoreductive surgery

5. Participants must have adequate organ and marrow function as defined below:

   leukocytes ≥3000/mcL absolute neutrophil count ≥1,500/mcL platelets ≥75,000/mcL total bilirubin ≤ institutional upper limit of normal (ULN) creatinine ≤ 1.5X institutional ULN

6. For participants with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated

7. Participants with a history of hepatitis C virus (HCV) infection must have been treated and cured. For participants with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load

8. Participants with metastases outside the peritoneal cavity are not eligible for enrollment

9. Participants with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial

10. The effects of PTX on the developing human fetus are unknown. For this reason, and because Taxane agents as well as other therapeutic agents used in this trial are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation. (Refer to Pregnancy Assessment Policy MD Anderson Institutional Policy # CLN1114). This includes all female patients, between the onset of menses (as early as 8 years of age) and 55 years unless the patient presents with an applicable exclusionary factor which may be one of the following:

    1. Postmenopausal (no menses in greater than or equal to 12 consecutive months)
    2. History of hysterectomy or bilateral salpingo-oophorectomy
    3. Ovarian failure (Follicle Stimulating Hormone and Estradiol in menopausal range, who have received Whole Pelvic Radiation Therapy)
    4. History of bilateral tubal ligation or another surgical sterilization procedure Approved methods of birth control are as follows: Hormonal contraception (i.e., birth control pills, injection, implant, transdermal patch, vaginal ring), Intrauterine device (IUD), Tubal Ligation or hysterectomy, Subject/Partner post vasectomy, Implantable or injectable contraceptives, and condoms plus spermicide. Not engaging in sexual activity for the total duration of the trial and the drug washout period is an acceptable practice; however periodic abstinence, the rhythm method, and the withdrawal method are not acceptable methods of birth control. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

    Men treated or enrolled on this protocol must also agree to use adequate contraception prior to the study, for the duration of study participation, and 4 months after completion of paclitaxel administration.

11. Ability to understand and the willingness to sign a written informed consent document

14) English and non-English-speaking participants

Exclusion Criteria:

1. Active infection such as pneumonia or wound infections that would preclude protocol therapy
2. Participants with unstable angina or New York Heart Association (NYHA) Grade II or greater congestive heart failure
3. Participants deemed unable to comply with study and/or follow-up procedures (i.e., cognitive impairment)
4. Participants with a known hypersensitivity to protocol systemic chemotherapy that was life-threatening, required hospitalization or prolongation of existing hospitalization, or resulted in persistent or significant disability or incapacity
5. Previous surgery that would preclude safe diagnostic laparoscopy with port placement
6. Participants who have not recovered from adverse events (AE) due to prior anti-cancer therapy (i.e., have residual toxicities > Grade 1) with the exception of alopecia
7. Participants who are receiving any other investigational agents
8. Participants with metastases outside the peritoneal cavity
9. History of allergic reactions attributed to compounds of similar chemical or biologic composition to PTX or other agents used in study
10. Participants with psychiatric illness/social situations that would limit compliance with study requirements Participants who are pregnant