What if Italy sortied while Germany concentrated its battleships?

What if the Italian fleet sortied at the same time as a concentrated German battleship operation?

Britain would have to retain major forces in the Mediterranean, with an eastern sortie occupying Cunningham and a western one pressuring Force H and Gibraltar.

Italy could plausibly sortie two or three capital ships while the German force threatened the Atlantic. An eastward move would occupy Cunningham's Mediterranean Fleet, preventing reinforcement elsewhere. A westward move could pressure Gibraltar and Force H, potentially retaining Renown, Ark Royal, or Nelson in that theater. The combined timing would therefore deepen Britain's force-allocation crisis even if the Italian fleet never joined the Atlantic battle.