Inclusion

1. Histologically or cytologically confirmed solid tumors including locally advanced/metastatic HR+ and HER2- breast cancer (post CDK4/6 inhibitor +/- ET, ≤ 2 lines systemic therapy), TNBC (1-3 prior lines including post ADC topo-1 payload), HNSCC (1-2 prior lines including post PD-L1/PD1 and platinum based therapy), and other solid tumor types (≤ 2 lines systemic therapy).
2. Male or non-pregnant, non-lactating female participants age ≥18 years.
3. Eastern Cooperative Oncology Group (ECOG) Performance Status (PS) of 0 to 1.
4. Participant must have at least 1 measurable lesion per Response Evaluation Criteria in Solid Tumors (RECIST) v1.1.
5. Life expectancy of >3 months, in the opinion of the Investigator.
6. Corrected QTcF <470 msec.
7. Adequate hematologic function.
8. Adequate hepatic function.
9. Adequate renal function.
10. Adequate coagulation profile.
11. Clinical sites must conduct fresh tumor biopsy or provide participant's archived tumor tissue sample.

Exclusion

1. History of another malignancy except for the following: adequately treated local basal cell or squamous cell carcinoma of the skin; in situ cervical carcinoma; adequately treated, noninvasive bladder cancer.
2. Known symptomatic brain metastases.
3. Significant cardiovascular disease within 6 months prior to start of study drug.
4. Evidence of an active systemic bacterial, fungal, or viral infection requiring treatment at the start of study drug.
5. Known active hepatitis B virus (HBV), hepatitis C virus (HCV), human immunodeficiency virus (HIV) or acquired immunodeficiency syndrome (AIDS).
6. Failure to recover to baseline severity or Grade ≤1 NCI-CTCAE v5.0 from acute non-hematologic toxicity.
7. Participants with NCI-CTCAE v5.0 Grade >1 neuropathy of any etiology.
8. Prior solid organ or bone marrow progenitor cell transplantation.
9. Prior high-dose chemotherapy requiring stem cell rescue.
10. Received systemic anticancer therapy within 28 days or within 5 half-lives (whichever is shorter) prior to the start of study drug.
11. Palliative radiation therapy within 14 days prior to the start of study drug.
12. Previously received extra domain B splice variant of fibronectin (EDB+FN) targeting treatments at any time prior to the start of PYX-201 treatment.
13. History of uncontrolled diabetes mellitus.
14. History of Stevens-Johnson syndrome or toxic epidermal necrolysis.
15. Participants with corneal epithelial disease, with the exception of mild punctate keratopathy
16. Participants with the best-corrected visual acuity in the worst-seeing eye worse than 20/100 (Snellen equivalent).
17. Participants with a history of (noninfectious) pneumonitis/ interstitial lung disease that required steroids, has current pneumonitis/ interstitial lung disease, or evidence of active pneumonitis on screening chest CT scan or suspected ILD/pneumonitis that cannot be ruled out by imaging at screening.