It is possible to do this. Your DNS entries will be a bit more complicated. I think the easiest thing for you to do is to add hosting here at Dreamhost for your domain and all your subdomains, and then manually edit the A records at your old host one at a time as you want to switch over. You can edit your /etc/hosts file on your local computer to view the Dreamhost sites before you switch each of the DNS entries over or you can use the dreamhosters subdomain method. This wiki article describes how to view your site before making the permanent DNS change.
Also, email delivery to the domain is controlled by your MX records, which are separate from the A records which "control" your hosting.
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