How do you say “Can I expand?”

"I'd like to expand on that, if I may." "Can I add more detail? " "To add to what she said..." "Just to add one more thought..." "One more thing to consider..." Or, popular in the business world: "Let's take a moment to dive into the details before we move on."

“Can I expand” is fine (“can I speak more detail about it” isn’t), though I’d probably say “can I expand on that” or “can I expand on it.” If you’re interested, some other options are: “can I elaborate” “can I explain” “can I go into detail” and “can I tell you more.”

Can I elaborate (on)

Agree with other answers, but my phrase would be "Can I expand upon it", rather than "on". "Can I expand" by itself would likely be just a little confusing but I'd get it, especially given the context.

It makes sense in enough context, but as others have said, "can I expand on this?" would be more clear and natural. Without that context, it sounds like you're asking if you yourself can literally expand (i.e. get bigger). Granted you'd almost certainly be understood (as you've learned), but it can often sound a little funny.

"can I speak more detail about it" is not natural. It doesn't even have to a question. Rather, just expand. Just keep talking. Or say that there is more to say. Here are a few options. Maybe instead: Let me explain... Can I expand on it/that? Expanding on that... Also... I'd like to expand on that. Additionally... I have some additional information to share. If you'd like more information on that, I have it. You'll also notice that...

"Elaborate" is precisely the word you want here. It is idiomatic and understood by almost everyone, and it has no ambiguity in its meaning.

You didn't invent this usage of "expand". It's fairly common to use some variation of "can I/you expand on this?" as a way to open a topic up to elaboration.

Use expound

It’s fine.

Can I elaborate

You can also use the phrase “elaborate” to mean “speak in more detail about it”.

“Can I add to that?” “Can I expand on that?” “You may want to consider the following points.”

My default would be, "I'd like to add to that."

“Can I expand on this/that” would be more natural. “To expand on (something)” means to explain in more detail. “To expand” means to physically grow larger lol