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 humburger do for the lunch?) or something is suffice ("そこにおくだけでいいです" / please just put it there [and I'll do the rest]/)
But "でもいい" has this added sense that there is something better/preferrable out there, but you are settling/asking for something less. This comes from the use of でも, which is a negative conjunction.
That is, お昼ごはんはハンバーガーでもいい? has a neuance that "I know you like something else" or perhaps "I don't konw if you like a humburger 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 here?"