The goal of Part 1 of this clinical research study is to find the highest tolerable dose of the combination of bosutinib and inotuzumab ozogamicin that can be given to patients with Philadelphia positive (Ph+) acute lymphoblastic leukemia (ALL) and chronic myeloid leukemia (CML) in the lymphoid blast phase that also expresses CD22 (a type of protein on the leukemia cell).