Approvals work fine with single level of 'Apply to Each' parallelism on. When approval action is in a nested 'Apply to Each' (parallelism turned on for both outer and inner loops), the loop cycles are not going on.
Issue can be reproduced in a simple flow;
Expected outcome from above sample flow:
So concurrency setting is only applied first item of outer loop, then behaves like first cycle of outer loop completed and moves on to next outer cycle. Changing "approval type" between anyone/everyone does not change the behavior.
It seems that you enabled Concurrency Control of Apply to each.
Using the concurrency control settings in for each loops can make sure all of the approvers receiver their request at the same time.
Have you bumped the degree of parallelism to the maximum?
I have made the following test.
In my scenario, I am going to get all the items in the list, then send an email with the details of a multiple selection enabled Choice column. A nested apply to each will be automatically created. A screenshot likes below. By the way, I have enabled the concurrency control and set it value to the maximum.
When the flow is triggered, it will send an approval email to both the two email addresses at the same time.
The issue you mentioned could not be reproduced by me.
Please share a screenshot of your flow to help reproduce.
Instead of using Set variable inside loop use compose action. the expression that you are using to set variable can be used in compose as well.
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