When you say "multiple domain transfers" what precisely do you mean? Many hosts offer the ability to host domains but it is unusual for a host to "throw in" domain transfers. If you already own the domains then you just change nameserver info.
Most of the other stuff you ask for, except for ASP and MS Access, is supported by almost every host. To do ASP and MS Access well, as HP-David pointed out, you will want a company that does Windows Web Hosting. I can't recommend any from personal experience but you can probably do a search for good windows hosting.
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