In general, "Would you like something else?," "Do you want something else?," and "Did you want something else?" are equivalent in meaning, but context and tone of voice are important.
The conditional "Would you ..." is considered most polite. Children are taught to use this phrasing.
The "Do you want ... " and "Did you want ... " are considered a bit abrupt in Canada.
In a different context, that of a manager finishing a meeting, there are differences.
- "Before we finish, would anybody have something to add (to say)?"
(polite request for last comments - note "something" as a positive element)
- "Before we finish, does anybody have something to add?"
(functional request for last comments - it is considered possible that someone will add a comment)
- "Before we finish, did anybody have anything to add?"
(perfunctory request for last comments - it is considered unlikely that anyone will add a comment - note past tense for an unreal present or future [like a type 2 condition] - note "anything" as a negative element)