In Part 2, subjects will be enrolled into an expansion cohort. Subjects will receive ASP2215 at the MTD established in Part 1 or recommended expansion dose, and will also receive remission induction, consolidation and maintenance therapy. The DLT observation period during the expansion cohort will be from the start of dosing of ASP2215 during the first remission induction treatment until Day 21 of the first consolidation cycle or before the start of the second consolidation cycle, whichever is sooner; as well as from the start of maintenance treatment until Day 28 of the second maintenance cycle. If testing at a dose level must be stopped, then a lower dose may be tested for remaining subjects to be enrolled.