This clinical trial is for men and women who have an advanced cancer that has not responded or has stopped responding to treatment with a class of drugs called programmed cell death protein-1 (PD-1) or programmed cell death-ligand 1 (PD-L1) inhibitors.
   
The aim of this research study is to understand the safety and efficacy of an experiment treatment called MT-8421. This study will look at MT-8421 by itself as well as when used with another drug, a PD-1 inhibitor, called nivolumab or OPDIVO® (brand name). This is the first research study using MT-8421 in humans. MT-8421 is experimental, meaning it has not been approved for the treatment of cancer by the United States Food and Drug Administration (FDA) and is not available to the public. Nivolumab has been approved by the FDA to treat many cancers.
   
The study will happen in 2 parts: Part A and Part B. The goal of Part A is to find the highest safe and tolerable dose of MT-8421. Then, a recommended dose will be determined in Part B. Both parts of the study will evaluate how well the study treatment works at treating a participant’s cancer.

Participants will be treated with either:

• MT-8421 intravenously (IV, through a needle in your vein or port) over 30 minutes on Day 1, Day 8, Day 15, and Day 21 of a 28-day cycle OR 
• MT-8421 intravenously over 30 minutes on Day 1, Day 8, Day 15, and Day 21 of a 28-day cycle and nivolumab intravenously for 1 hour on Day 1 of each 28-day cycle, starting at Cycle 2. 

 Participants will be treated until their cancer gets worse, they become too sick to continue, their cancer responds and they no longer need treatment, they no longer want treatment, or their study doctor decides it is in their best interest to stop study treatment with MT-8421.
   
After study treatment is stopped, the study doctor will evaluate participants every 3 months for up to 2 years.