Completion at point with empty prefix?

[Dmitry Gutov]

In the mode I'm writing, in certain contexts, there can be only a
limited set of completions when the function call has no sender.

So I don't actually need a prefix to show the user the set of methods
they can call at the point, and supporting that should increase the API
discoverability.

How do I set that up? I have a completion-at-point function working, but
if START is the same as END in the returned list, `completion-at-point'
just says "No symbol here".

I tried inserting space after point and returning END = START + 1, made
no difference.

--Dmitry