A First-in-human Study of Multiple Doses of BB-1701 in Subjects With Locally Advanced/Metastatic HER2 Expressing Solid Tumors

Inclusion Criteria: 1. Willing and able to provide written informed consent for the trial. 2. Male or female subject ≥ 18 years. 3. Patients must have a histologically or cytologically confirmed locally advanced unresectable or metastatic HER2 expressing solid tumor(s) for which no curative therapy is available or tolerable 4. Patients with breast cancer who are estrogen receptor (ER) and/or progesterone receptor (PR) positive and in whom hormonal therapy is indicated (e.g., patients with positive ER and/or PR without rapidly progressive or extensive visceral metastases) must have received at least 1 prior line of hormonal therapy 5. Patients must have at least one measurable lesion as defined per RECIST Version 1.1. 6. Patients must have a brain MRI (breast cancer only for part 2 cohort expansion) for the status of brain metastasis within 28 days prior to the first dose. Those with asymptomatic or stable CNS metastases are eligible for participation. However, patients with symptomatic and 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 should not be enrolled in the study. 7. Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. 8. Life expectancy ≥12 weeks. 9. Subjects (women of childbearing potential and males with fertile female partner) must be willing to use currently accepted reliable contraception method throughout the treatment period and for at least seven months following the last dose of study drug. 10. Patients (women of childbearing potential and males with fertile female partner) must be willing to use currently accepted reliable contraception method throughout the treatment period and for at least six months following the last dose of study drug. 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. 11. Washout period required from the end of prior treatment to the first administration of the study drug 12. Be able to provide a fresh formalin-fixed, paraffin-embedded (FFPE) tumor tissue block, or 5-10 non-staining tumor slides (cohort 4 should be within 2 years) for evaluation or confirmation or exploratory diagnostic tests of HER2 status. Exclusion Criteria: 1. Is receiving cancer therapy (chemotherapy or other systemic anti-cancer therapies, immunotherapy, radiation therapy, or surgery) at the time of enrollment. 2. Has not recovered from adverse events (e.g., not returned to baseline or grade 0\~1) due to a previously administered agent. 3. Had major surgery within 4 weeks before dosing, or will not have fully recovered from surgery; or has surgery planned during the time the subject is expected to participate in the study or within 4 weeks after the last dose of study drug administration 4. Use of any investigational anti-cancer drug within 28 days before the first investigational product administration. 5. Has received prior cumulative doxorubicin dose \> 360 mg/m² or equivalent 6. Has grade 2 or higher peripheral neuropathy, or had a history of grade 3 or higher peripheral neuropathy or had a history of treatment discontinuation due to peripheral neuropathy 7. Has an 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 (e.g. Chronic Obstructive Pulmonary Disease). 8. Has 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. 9. Any other serious underlying medical conditions, including but not limited to, uncontrolled diabetes mellitus, active uncontrolled infection, active gastric ulcer, uncontrolled seizures, cerebrovascular incidents, gastrointestinal bleeding, severe signs and symptoms of coagulation and clotting disorders 10. Patients has clinically significant cardiovascular disease. 11. QTc interval \>/= 450 msecs for male or \>/= 470 msecs for female \[Fridericia's formula: QTcF=QT msec/(RR sec)0.33). 12. Current dyspnea at rest due to complications of advanced malignancy, or other diseases requiring continuous oxygen therapy. 13. Any other serious underlying medical conditions, including but not limited to, psychiatric, psychological, familial or geographical condition that, in the judgment of the investigator, may interfere with the planned staging, treatment and follow-up, affect subject compliance or place the subject at high risk from treatment-related complications. 14. History of seropositive status for human immunodeficiency virus (HIV) at any time before the start of treatment as determined by presence of anti-HIV-1 or anti-HIV-2 antibodies. Testing for seropositive status during Screening will be at the discretion of the investigator in participants without previously reported results. 15. Active hepatitis B, or hepatitis C infection. Participants will be tested for hepatitis C virus (HCV) and hepatitis B virus (HBV) at screening: 16. History of life-threatening hypersensitivity, or known to be allergic to protein drugs or recombinant proteins or excipients in BB-1701 drug formulation, or intolerance to trastuzumab or eribulin. 17. Females who are pregnant (positive beta-human chorionic gonadotropin positive \[β-hCG\] test) or breastfeeding. 18. Concurrent condition that in the investigator's opinion would jeopardize compliance with the protocol. 19. Unwillingness or inability to follow the procedures outlined in the protocol.