I'm using ProfiMail (and have been for some years on Symbian earlier...), and it lets you switch back and forth (I sometimes have to compile some information I have in various files/locations on my phone, and as long as I switch by going to the desktop or by alt-tabbing). (And I assume it works with keyboard shortcuts too, if one has that set up with an appropriate app.) If I need information from another mail, I of course WILL have to save a draft and open it again.
I find it operates more reliably on the Cosmo than it did on the Gemini, but it handles something like 20 mail-accounts, of which several has several thousand mails in both inbox and sent-folder for me, so that is probably the main reason for that anyway... It does have some bugs, like replying to a mail in the "sent" folder, reply to yourself (which you can get around by using "reply all" and take yourself off the list). It used to handle that correctly before, I'm sure.
But one of the main reasons I prefer/swear by it, is because of their three panel view: Left side, mail-accounts, top right, mails in current box/folder, and bottom right, mail preview (I seldom view mails in fullscreen at all, I just use the preview). And it supports quite a few keyboard shortcuts (but believe it supported more on my Nokia E90/E7...).