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If multiple phases are added to the same point in your turn, the most recently created phase happens first. For example, say Obeka deals combat damage and its ability resolves during your combat damage step, giving you two additional beginning phases each containing an upkeep step after this combat phase. During end of combat, another effect gives you an additional combat phase after this combat phase. The additional combat will happen first, followed by the additional beginning phases containing the two upkeep steps.
After the beginning phases containing the additional upkeep steps, the game proceeds to the next phase as normal, which is likely to be your postcombat main phase (unless something has added even more phases; see below).
Abilities that trigger "at the beginning of [your] upkeep" will trigger at the beginning of each additional upkeep step as well.
Since the upkeep step can only occur during the beginning phase, getting one or more additional upkeep steps outside of the beginning phase actually means you get an additional beginning phase for each of those upkeeps after this phase. In those beginning phases, the untap and draw steps will be skipped.
The beginning phases containing the additional upkeep steps occur after the current combat phase ends. The last step of the combat phase is the end of combat step.
