The short answer is: you can’t do it.
From T-SQL there is no way to access multiple results of a nested stored procedure call, without changing the stored procedure as others have suggested.
To be complete, if the procedure were returning a single result, you could insert it into a temp table or table variable with the following syntax:
INSERT INTO #Table (...columns...)
EXEC MySproc ...parameters...
You can use the same syntax for a procedure that returns multiple results, but it will only process the first result, the rest will be discarded.