Like you, I have several different e-mail accounts (all "remote") and send through a number of different mail servers (depending on the account, of course). I use mutt 99% of the time, on my laptop, wherever I may be (home, friends' homes, customer sites, public hotspots, etc.). I couldn't (easily) do it with just mutt but with the help of various external tools (such as offlineimap, msmtp, and notmuch) I have no problems or hoops to jump through on a daily basis to make things work.