This study has four parts. Part 1 is a dose escalation of BDC-1001 as a single agent to determine the maximum tolerated dose (MTD) recommended for Part 3 and Phase 2 (RP2D). In Part 3, the selected dose will be administered as monotherapy to patients with selected advanced malignancies. Part 2 is a dose escalation of BDC-1001 in combination with pembrolizumab to determine the maximum tolerated dose (MTD) recommended for Part 4 and Phase 2 (RP2D). In Part 4, the selected dose will be administered in combination with pembrolizumab to patients with selected advanced malignancies.

