A reasonable, professional negotiation request usually does not make you look bad by itself.

The risk comes from pushing repeatedly on standardized terms, inventing leverage or treating the offer as an adversarial negotiation.

Ask once where you have a real question or constraint, explain the reason clearly and listen to what is actually flexible.

If the firm says a term is fixed, decide based on the offer rather than continuing to pressure the recruiter. For more detail, see the guide to choosing between consulting offers.

I asked one focused question about relocation and the recruiter was completely normal about it.

yeah, I declined one offer with a short thank-you note and stayed in touch with the recruiter.

In my case the base was fixed, but timing had some flexibility, so it was still worth asking.

I declined one offer with a short thank-you note and stayed in touch with the recruiter.