I have been successful in adding an ASM for safety reasons, and when I find myself having to be in two places at the same time:
If I feel we need a set of eyes on a potentially unsafe situation - open traps, tracking/ flying scenery, really anywhere we have actors in a blind spot. The ASM can either call a hold to a move, or call a clear before we begin a move.
If an actor has to leave the stage/backstage area, for a rear of house entrance or any non-standard entrance. The ASM can keep the path clear, deal with any interference on the way, help with costume changes/ prop handoffs on the way, provide a flashlight in dark areas, carry a water bottle, page doors, cue the actor entrance, and report back to me if there are any problems en route.
If you have any pyro & no pyrotech on show call, then I want one person who has eyes on an open flame from when it's lit to when it's extinguished, and then they confirm it's really extinguished. Cigars, pipes, cigarettes, candles, etc.
I have also added an ASM if I find that stagehands are placed in a situation of having to make a judgement call. They should only have to take a cue from the SM or take a clear audio/visual cue. If they can't be on com or have a cue light, then an ASM should be there to signal them. So, a blackout is a good non-called cue. But, "whenever you feel the applause is starting to die down" is an SM/ASM call.
Lastly, any show which involves animals or children will likely need an ASM in addition to the handler/ wrangler because they often have different show call/ load-in & load-out times, sometimes during the show, and you'll want an assistant who can confirm they are in the building and assist as needed. Also, the handler/ wrangler has someone they can contact if they are delayed, and they have someone to talk to if they have questions or concerns in the moment.
Those are situations I have come across, and it's also how I can now list "duck wrangling" on my resume. Thank you, Lincoln Center Festival!
-Colleen