Study of EO-3021 in Adult Patients With Solid Tumors Likely to Express CLDN18.2

Key Inclusion Criteria: * Availability of tumor tissue for evaluation of biomarker * Patients enrolled to expansion must have tumors expressing CLDN 18.2 based on central prospective IHC testing. * Histologically and/or cytologically confirmed diagnosis of advanced metastatic gastric/GEJ adenocarcinoma not amenable to resection or radiation therapy with curative intent •≥ 18 years of age * ECOG performance status (PS) 0 or 1 at Screening * Progressed on or after standard therapy, or are intolerable of available standard therapy, or there is no available standard therapy * In dose escalation, there is no limit on the number of prior lines of therapy. * In expansion, for EO-3021 monotherapy, at least 1 but no more than 3 prior lines of therapy in the advanced/metastatic setting is allowed * In expansion, for EO-3021 in combination with ramucirumab, only 1 prior line of therapy in the advanced/metastatic setting is allowed. Prior fluoropyrimidine and platinum-containing chemotherapy is required * In expansion, for EO-3021 in combination with dostarlimab, no prior systemic therapy in the advanced/metastatic setting is allowed. * Have at least one measurable extra-cranial lesion as defined by RECIST v1.1 * Adequate organ function * Life expectancy \> 12 weeks * Ability to understand the nature of this study, comply with protocol requirements, and give written informed consent * Willingness of men and women of reproductive potential to observe conventional and effective birth control for the duration of treatment and for 6 months following study completion (or longer if required by local regulation) Key Exclusion Criteria: * Pregnant or breastfeeding * Symptomatic or untreated brain metastases * Have previously received CLDN18.2 antibody drug conjugates (ADCs) or any ADC containing an auristatin payload (prior monoclonal antibody against CLDN18.2 may be eligible) * Have peripheral neuropathy Grade ≥2 * Have history of non-infectious pneumonitis/interstitial lung disease * Have diagnosis of another malignancy, or history of systemic treatment for invasive cancer within last 3 years. Note: Patients with Stage I cancer who have received definitive local treatment and are considered unlikely to recur are eligible. Diagnosis of non-melanoma skin cancer, carcinoma in situ of the cervix or breast, or noninvasive tumor does not affect eligibility * Have active ocular surface disease at baseline (based on screening ophthalmic examination) as defined as symptomatic or Grade ≥2 disease involving the cornea * Have history of Grade ≥2 gastritis * Have serious concurrent illness or clinically relevant active bacterial, fungal or viral infection * Have a history of several allergic and/or anaphylactic reactions to known chimeric, human, or humanized antibodies, fusion proteins or known allergies to components of EO-3021, ramucirumab, or dostarlimab * Clinically significant cardiac disease, including but not limited to symptomatic congestive heart failure, unstable angina, acute myocardial infarction within 6 months of planned first dose, or unstable cardiac arrhythmia requiring therapy (including torsades de pointes) * Have history of allogenic hematopoietic stem cell transplantation or solid organ transplantation with ongoing systemic immunosuppressive therapy * Received any live vaccine within 30 days of enrollment * Patients who are not appropriate candidates for participation in this clinical study for any other reason as deemed by the Investigator * Expansion only: Have HER2+ disease as defined by American Society of Clinical Oncology-College of American Pathologists guidelines for gastric/GEJ adenocarcinoma * Ramucirumab Arms Only: Received prior treatment with ramucirumab and other VEGFR2 inhibitors * Dostarlimab Arms Only: Prior treatment with immune checkpoint inhibitors (ICI) including dostarlimab and other anti-PD-1, anti-PD-L1, etc.