SMP-3124LP in Adults With Advanced Solid Tumors

Inclusion Criteria: \- Histologically or cytologically-confirmed cancer that is advanced, recurrent, or metastatic with the following origins, and whose disease progressed on standard therapy and for whom there are no alternative therapies that may confer overall survival benefit. For patients in the Dose Escalation part: 1. Platinum-resistant ovarian cancer * Histologically diagnosed ovarian, fallopian tube, or primary peritoneal cancer, with predominantly high-grade (Grade 2 or 3) epithelial features (serous and clear cell) * Platinum resistant is defined as relapsed within 6 months after the last dose of platinum-based therapy 2. Triple negative breast cancer - ER- and PR-negative with HER2 negative * HER2 negative is defined as one of the following: 0 or 1+ by IHC, or if IHC 2+, then in situ hybridization is negative per the ASCO-CAP HER2 guidelines * ER- and PR-negative is defined as \< 10% of cells expressing hormonal receptors by IHC, as per standard guidelines 3. Squamous cell carcinoma of the anus \- Patient with locally advanced ineligible for surgery is allowed. 4. Squamous cell carcinoma of the head and neck 5. Non-small cell lung cancer (NSCLC: adenocarcinoma, large cell, and squamous cell carcinoma) 6. Uterine serous cancer (recurrent or persistent) For Patients in the Dose Expansion Part: 7. Cohort A: PROC (same as above) 8. Cohort B: TNBC (same as above) 9. Cohort C: SCCA (same as above) * ECOG performance \</= 2 at screening * Recovered from any prior treatment related toxicities * Adequate organ function as evidenced by: a. Hemoglobin \>/= 9 g/dL (transfusion or use of erythropoietin to obtain this are not permitted) b. Absolute neutrophil count \>/= 1500 uL (platelet transfusion not allowed to achieve this) c. Platelet count \>/= 100 x 10 (platelet transfusion not alled to achieve this) d. Bilirubin \</= 1.5 x ULN (or \</= 3.0 x if ULN if Gilbert's syndrome) e. AST and ALT \</= 3.0 x ULN (or \</= 5 x ULN if the liver has tumor involvement f. Calculated creatinine clearance \>/= 60 mL/min using Cockcroft-Gault formula * Patient is non-fertile or agrees to use adequate methods of contraception or agrees to refrain completely from heterosexual intercourse during the study and for 6 months (for female and male patients alike) after the last dose of study intervention. * May be HIV positive if the following conditions are met: 1. CD4 + T-cell count \>/= 350 cells/uL 2. HIV viral load \< 400 copies/ml prior to enrollment 3. No history of acquired immunodefficiency syndrome (AIDS) defining opportunistic infections * Known hepatitis B infection mush have negative serum HbsAg. Patients with known hepatitis C virus infection must have a viral load below the limit of quantification Japan sites only: HBc antibody or HBsantibody tests should be performed if HBsAg is negative. If HBc antibody or HBs antibody tests are positive, HBV DNA quantitative tests should be performed to confirm that HBV DNA is negative. Exclusion Criteria: * Patient has received prior treatment at any time with a cell cycle checkpoint inhibitor (eg, CHK1 and/or CHK2, WEE1, or ATR inhibition) * Patient has a known allergy or sensitivity to any component of SMP-3124LP, including the inactive ingredients * Patient has received treatment with systemic anticancer therapy, radiotherapy, or investigational therapy within 14 days prior to Study Cycle 1 Day 1. (Palliative radiotherapy with a limited field of radiation within 2 weeks will be permitted.) * Patient has undergone a major surgical procedure ≤ 28 days, or minor surgical procedure ≤ 7 days, prior to Cycle 1 Day 1 * Patient has used strong CYP1A2 or 2D6 inhibitors within 14 days or 5 half-lives, whichever occurs first, prior to Cycle 1 Day 1 (examples of restricted CYP1A2 and CYP2D6, P-gp, and/or BCRP inducers, inhibitors, or substrates are presented in Table 16) * Patient has central nervous system metastasis or leptomeningeal disease * Prior or concurrent malignancy whose natural history or treatment would have a significant potential to interfere with the safety or efficacy assessments of the investigational regimen * Patient has an abnormal ECG that is clinically significant, including a corrected QT interval (corrected using Fridericia's correction formula \[QTcF\]) \> 470 msec; and/or a history of Torsade de Pointes * Patient has a left ventricular ejection fraction \< 45% by echocardiogram (ECHO) * Patient has clinically significant cardiac disease including heart failure (eg, New York Heart Association, Class III or IV) * Patient has an active, uncontrolled, bacterial, viral, or fungal infection requiring parenteral antimicrobial within 1 weeks prior to Cycle 1 Day 1 * Patient is pregnant (as evidenced by a positive serum or urine pregnancy test) or is breastfeeding. Female breastfeeding patients may be enrolled if they interrupt breastfeeding. Breastfeeding should not be resumed for at least 6 months after the last dose of study drug. For sites in Japan only: In addition to the above, any patient deemed likely to be pregnant based on medical interview will be excluded from the study. * Patient with ovarian cancer 1. Has a history of bowel obstruction related to their underlying disease within 3 months prior to Study Day 1 2. Has platinum-refractory disease. Platinum refractory is defined as progression during platinum-based chemotherapy * Patient has any other medical or psychiatric condition that, in the opinion of the investigator, might interfere with their participation in the trial or interfere with the interpretation of trial results * Patient is taking a prohibited medication at baseline.