I'm trying to figure out the best way to ask for help on someone else's behalf, like in "Could you help my friend with the elevator?". For myself, I would think that something like "エレベーターを手伝ってくれませんか" would be fine, but I'm not sure how you'd change the target of the help to someone else in that case.
In Xを手伝う, X can be:
- a person to be helped (友人を手伝う)
- a "doable" action or a nominalized verb (掃除を手伝う; 宿題を手伝う; 立ち上がるのを手伝う)
- (uncommon) a room/place when it is clear from the situation that there is a large task there (厨房を手伝う; 倉庫を手伝う)
If the action is "doable" (i.e, can be used with (を)する), you can simply say 彼女の英語の勉強を手伝ってくれませんか, 父親の仕事を手伝ってください, and so on. If the action is a nominalized verb, you can say 彼が立ち上がるのを手伝ってください and so on.
However, エレベーター is not an action, and 彼のエレベーターを手伝う makes no sense. エレベーターを手伝う may be natural if there are several tasks going on and installing/fixing an elevator is one of them, but unless you're a worker involved in the construction of a building or a concert venue, you'll never get a chance to say it.
Instead, you can insert a nominalized verb and say 友人がエレベーターに乗るのを手伝ってくれませんか. Note that a long sentence like this is only necessary if you're asking this in an email. If you're actually in front of an elevator with your friend, something like 手伝ってください or even 乗せてください can be enough.