For example in the sentence: 書くだけでいいですか.
The meanings are quite similar, but there's a subtle difference.
Both phrases involve settling for something, or one person making a choice on behalf of another:
お昼ごはんはハンバーガーでいい？ "Would a hamburger do for lunch?" Or something is sufficient:
そこにおくだけでいいです "Please just put it there [and I'll do the rest.]"
でもいい has an added sense that there is something better or preferable out there, but you are settling, or asking, for something less. This comes from the use of
でも, which has a negative conjunction.
お昼ごはんはハンバーガーでもいい? has a nuance of, "I know you like something else," or perhaps, "I don't know if you like a hamburger or not." Another example would be:
名前を書くだけでもいいですか？ and this would mean something like, "[You want to me to put down my address for this petition, but] would it be OK if I just write my name?"