|Oh boy. As far as I understand CARs you can indeed have an M2 / E license. You can not have an M1 / M2 / E license.
I know three folks with an M2/E license, so they do exist and I have seen more than one. One thing they have all mentioned is that as far as they know if they go out and get an M1 they would loose the E on their license.
There are two ways to get an M2/E license that l know of. Method one: go and get an E license as per the usual school + time + tasks method, and then go and do the M school (either in person or via ICS) and then go fill a logbook of M tasks. Method two: Go and get an M license via the usual school + time + tasks method, and then once done take the avionics school (as far as I know the only ones being offered at this time are go to school in person style courses) and then go and do a book of E tasks. I know two people that used method one, and the third guy I've never did hear how he went about it.
If you have both M1 an M2 Transport will not issue an S or an E rating, as "Individuals who hold both an M1 and M2 rating will not be issued any additional ratings (e.g. E or S ratings), as those privileges are already held within the scope of the combined M1/M2 rating privileges." Be careful though, this point has traditionally been a text book example of "clear as mud", some say that means with a M1/M2 license your good to sign specialized S and E work, others say you can only sign out specialized S or E work if you can prove that you've had the applicable S or E basic training to go with your M license. I've never been able to get a clear answer on this despite searching through CARs on several occasions.
My personal opinion is if I had an M1/M2 license as it is now I think I technically could sign out specialized S and E work but I would most definitely shy away from signing anything of the sort as I don't feel I've had the appropriate training or experience for it. The E guys I know are one heck of a lot smarter than I am when it comes to E type work so I'll happily leave them to do their thing. Just because you can doesn't mean you should.
As per Canadian Aviation Regulations Standard 566.03:
"(9) Additional ratings.
An AME may apply for additional ratings by meeting the requirements specified in 566.03. Credit will be granted for any requirements that were met in qualifying for the currently held ratings.
Individuals who hold both an M1 and M2 rating will not be issued any additional ratings (e.g. E or S ratings), as those privileges are already held within the scope of the combined M1/M2 rating privileges.
(10) Obsolete ratings.
AMEs who held ratings under the preceding licence system, that have no direct equivalents, or for which no designators have been established in the new system, will have the ratings entered on their licence in plain text. Examples of this include Balloons, Propellers, and Dynamic Components."