Nope, you assign blockers all at the same time, with no room for playing spells or abilities in between.
For MTM, at the beginning of your upkeep the “discard or sacrifice” trigger will go on the stack. At that point you can respond to the triggered ability by playing the other abilities, and they will resolve before the triggered ability.
(Note that this is your first chance to play spells or abilities during your turn, there is no “after untap but before upkeep”)
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