In theory, you could use many other verbs, but you won't hear natives do this very often. In colloquial English there are a few usages which are more common. Also, most native English speakers use the conditional tense with this type of phrase. For example: Don't you think it would be better if we finished cleaning the house first? 'I couldn't agree more!' Are you enjoying your new life in Australia? 'It's incredible, I couldn't be happier!

You could, and it would be kind of funny, but not very common. Couldn't agree more is common.