The main goal of this study is to evaluate how safe and tolerable RNDO-564 is and to identify the best dose of RNDO-564 as a single agent and in combination with pembrolizumab. The study is focused on participants with certain solid tumors that are in an advanced stage and have certain tumor makers. This will be done by measuring the side effects that participants experience and how severe they are. Additionally, the study will evaluate how RNDO-564 moves into, through, and out of the body and how the treatment affects the body.

The second goal of this study is to evaluate how well RNDO-564 works by itself or in combination with pembrolizumab at treating participants' cancer. This will be done by measuring the number of participants who respond to the treatment. The length of time where the tumor does not grow or spread will also be measured.

Participants will take RNDO-564 weekly on Days 1, 8 and 15 of a 21 day cycle. Participants in the combination arms will take RNDO-564 as described with pembrolizumab every 3 weeks.

The study will consist of four stages: 1) single agent dose escalation, 2) single agent dose optimization, 3) combination dose escalation and 4) combination dose optimization.

Stages 1 and 3 are dose escalation to investigate the safety and tolerability of increasing doses of RNDO-564 as a single agent and in combination with standard pembrolizumab treatment. Participants will be enrolled who have one of the following advanced solid tumors associated with Nectin-4: locally advanced/metastatic urothelial cancer (la/m UC), cervical cancer (CC), head and neck cancer (HNSCC), esophageal cancer (EC), gastric (GC) and gastroesophageal junction cancer (GEJ), triple negative breast cancer (TNBC), and non-small cell lung cancer (NSCLC). The cancer must not have responded well to previous cancer treatments. Stages 1, and 3 will be non-randomized.

Stages 2 (i.e., RNDO-564 single agent) and 4 (i.e., RNDO-564 in combination with pembrolizumab) are dose optimization and proof-of-concept stages to further investigate the safety and tolerability of at least 2 doses of RNDO-564 as a single agent and in combination with standard pembrolizumab treatment, and to investigate preliminary anti-tumor activity. Stages 2 and 4 will enroll participants with advanced urothelial cancer only. The cancer must not have responded well to previous cancer treatments. Participants will be randomized (1:1) into one of two arms which will evaluate two dose levels (as selected from Stages 1 and 3).

The study consists of a screening period, a treatment period, an end of treatment visit, a safety follow-up visit, and 60 and 90 days telephone follow-up after ending treatment. The treatment period will last for a maximum of 2 years.

Inclusion Criteria:

1) Eligible tumor types: Histologic documentation of incurable, locally advanced or metastatic solid tumors for which established standard systemic therapies are no longer effective (participant must have experienced progressive disease), are not tolerated, or in the opinion of the Investigator have been considered ineligible for a particular form of standard therapy on medical grounds or have been declined by the participant, with these tumor subtypes:

A. Monotherapy and Combination Dose Escalation Arms:

• RR la/mUC: Participants with urothelial cancer (transitional cell) with squamous differentiation or mixed cell types are eligible. Participants with upper tract disease, e.g., involving ureters, or renal pelvis, are eligible. Participants may have had up to 2 prior monomethyl auristatin E (MMAE)-containing therapies, assuming any existing peripheral neuropathy is Grade 2 or less.
• NSCLC
• HNSCC
• CC
• GC and GEJ
• EC
• TNBC

B. Dose Optimization (Monotherapy and Combination Arms):

• Limited to participants who have RR la/mUC,

• Participants may have had up to 2 prior MMAE-containing therapies, assuming any existing peripheral neuropathy is Grade 2 or less 2. Participants must have measurable disease per response evaluation criteria in solid tumors (RECIST) v1.1.

  3. Adequate organ function

Exclusion Criteria:

1. For Nectin-4 targeted agents (approved or investigational)

   • > one prior Nectin-4 targeted agents

2. Peripheral neuropathy > Grade 2

3. Participants with a history of, or with active, inflammatory skin disease, such as eczema, psoriasis that required or currently require biologics or oral steroids to control disease are ineligible.