The study consists of two phases: dose-escalation (Phase I) and cohort expansion (Phase II).

Phase Ia is a dose escalation study to assess the safety and tolerability, and to determine the MTD or MAD and RP2D of BB-1705.

Phase Ib is a cohort expansion study to explore one or more RP2Ds to further assess safety, tolerability, pharmacokinetics, and preliminary anti-tumor activity. Patients with locally advanced and unresectable or metastatic solid tumors who have progressed on prior lines of standard of care therapies will be enrolled in this study if eligible.

Inclusion Criteria:

1. Willing and able to provide written informed consent form (ICF) for the trial.
2. Adult patients ≥ 18 years at the time of signing ICF.
3. Patient must have a histologically or cytologically confirmed, locally advanced, unresectable, or metastatic solid tumors:
4. At least one measurable lesion as defined per RECIST Version 1.1.
5. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1.
6. Life expectancy ≥12 weeks.
7. Adequate organ function as indicated by the following laboratory values (had not received blood transfusion, EPO, G-CSF, or other medical support within the 14 days before the administration of BB-1705):
8. Women of childbearing potential and males with fertile female partner must be willing to use currently accepted reliable contraception method throughout the treatment period from ICF signed and for at least 6 months following the last dose of BB-1705. These measures include, but are not limited to, oral or implantable injections of hormonal contraceptives; intrauterine birth control ring or placement of IUS intrauterine device); or use of barrier methods such as condoms or septum and spermicide products. Postmenopausal women over 50 years of age must have been amenorrheic for at least 12 months to be considered of non-childbearing potential. Women of childbearing potential must have a negative pregnancy test ≤ 7 days prior to the first dose of investigational product.

Exclusion Criteria:

1. Receiving cancer therapy (chemotherapy or other systemic anti-cancer therapies, immunotherapy, radiation therapy, or surgery) at the time of enrollment
2. Prior history of other malignancies.
3. Not recovered to baseline or ≤ grade 1 adverse events from prior anti-cancer treatment.
4. Major surgery within 4 weeks and minor surgery within 2 weeks before the first dose or not fully recovered from surgery; or surgery planned during the time the patient is expected to participate in the study
5. Grade 2 or higher peripheral neuropathy.
6. Active pneumonitis/interstitial lung disease (ILD), a history of pneumonitis/ILD that required systemic steroids, received radiotherapy to lung field within 12 months before the first dose of study intervention, or current clinically relevant-lung disease
7. Symptomatic or untreated CNS metastases, or those requiring ongoing treatment for CNS metastases, including steroids (>10 mg of prednisone or 4 mg of dexamethasone) and antiepileptic agents.
8. Any other serious ongoing underlying medical conditions, including but not limited to, uncontrolled diabetes mellitus, active uncontrolled infection, vaccination within 4 weeks, active gastric ulcer, uncontrolled seizures, cerebrovascular incidents within 6 months of study entry, gastrointestinal bleeding within 3 months of study entry, severe signs and symptoms of coagulation and clotting disorders.
9. QTc interval ≥450 ms for male or ≥470 ms for female (Fridericia's formula) and patients with congenital long QT syndrome.