To answer the question, though —
No, it's not possible to split the mailboxes on a domain across multiple email services. Only one email service (e.g, DreamHost, Google Apps, or whatever else) can be configured to receive incoming mail for your domain at a time.
(There are some ways to partially work around this by having the "main" email service for a domain forward some mail on to another email service using an alternate domain name. It's all rather tricky and fragile, though, and I wouldn't recommend that you go this route unless you absolutely have to.)