Learn Hardcore Chinese: nǐ kěyǐ zài shuō ma?

吗 turns a statement into a yes–no question. With 吗, the intonation is usually level or slightly falling. You can sometimes ask with rising intonation alone, but for clear, polite, textbook-standard requests like this, keep 吗.

Which is better here: 可以, 能, or 会?

可以 (kěyǐ) asks for permission or makes a polite request (may/could), which fits best here.
能 (néng) focuses on ability/possibility; it also works but sounds a bit more about capability than permission.
会 (huì) means know how/will; 你会再说吗？ is odd here (it could mean will you say it again).

Does 再 mean “again” here? How is it different from 又 or 重新?

Yes, 再 means “again” for a future or requested repetition. 又 typically means “again” for past or habitual events. 重新 means “afresh/from the beginning,” e.g., 重新说一遍 = restate from scratch.

Should I add 一遍 or 一次 after 说? Is it wrong to omit it?

It’s not wrong to omit it; context supplies “that.” However, many speakers add it for naturalness and clarity: 你可以再说一遍吗？ or …再说一次吗？. 一遍 emphasizes a full run-through; 一次 is a neutral count of times.

Can I say 再说一下? What’s the difference from 再说一遍?

再说一下 is a softer, lighter request (“say it again a bit/briefly”), thanks to 一下. 再说一遍 is the most common, neutral “say it again (once).” Both are polite in this question pattern.

Can I replace 说 with 讲?

Yes in many contexts. 说 is the general “say/speak,” widely used on the Mainland (再说一遍). 讲 can sound more like “speak/tell/explain” and is very common in Taiwan (再讲一次). Both are understood.

What’s the correct word order? Can I move 再 or 你 around?

Natural order is Subject + Modal + Adverb + Verb + Particle: 你可以再说吗？. You can drop 你 if context is clear: 可以再说吗？. Don’t say 你再可以说吗？ or 你可以说再吗？—those are incorrect.

How do I pronounce this with tones? Any tone sandhi to watch?

A common pronunciation is: nǐ kéyǐ zài shuō ma (3–2–3–4–1–neutral). 可以 is often kéyǐ (first syllable becomes a rising tone). 吗 is neutral. Also, 说 shuō uses the retroflex “sh,” not the plain “s.”

Can I use 呢 instead of 吗?

Not here. 呢 doesn’t make a yes–no question by itself. Use 吗 for this kind of polite yes–no request.

How do I make this more polite or formal?

Good options:

请再说一遍，可以吗？
麻烦你再说一次。
不好意思，您可以再说一遍吗？
Using 请, 麻烦, 不好意思, and 您 all increase politeness.

Is there any ambiguity with 再说 meaning “let’s talk about it later”?

再说 can mean “talk about it later” in sentences like 再说吧. In your sentence, with 可以…吗 and the verb 说 directly modified by 再, it clearly means “say (it) again,” not “discuss later.”

Can I drop the subject and the particle, like just 再说一遍?

You can, but 再说一遍 on its own is an imperative and may sound blunt. Add a softener for politeness: 请再说一遍 or 麻烦再说一遍.

How do I ask for both repetition and slower speed?

Say 你可以再说一遍，慢一点吗？ or 你可以说慢一点，再说一次吗？. Common and concise: 可以再说一遍慢一点吗？

How do I address one person politely or a group?

To one person politely: 您可以再说一遍吗？
To a group: 你们可以再说一遍吗？

How would people naturally reply to this request?

Typical positive answers: 可以, 好, 没问题. Then they repeat it. A soft refusal might be 现在不太方便，等一下可以吗？