Name a usable limit
Write “Choose a restaurant where a main course costs up to $20.” If someone wants to suggest a more expensive place, give everyone a chance to decline privately. Updating the restaurant choice does not require an explanation of one person's finances in the group notes. Specify whether the limit covers the main course alone or the whole outing. A restaurant that meets the menu limit may still miss a total that includes travel or extras.
Compare two suggestions
Suppose the group limit is $25 per person for food. One venue generally fits the limit and another fits only if each person chooses a starter instead of a main course. Ask the group whether that narrower choice is acceptable. The person who proposed the limit need not explain a private financial circumstance for the group to honor it.
When someone offers to cover the difference
Confirm privately what the offer covers and whether the recipient wants to accept it. A vague promise to “sort it out later” can leave someone facing an expense they did not agree to. Put the final venue and agreed payment arrangement in the shared plan once everyone accepts.