It doesn’t exactly improve your game to learn another character, but if you choose the right one to complement your main then it can help when it comes to counter-picking. It’s also good to have a character that plays completely differently from your main for when you get bored.
I would NEVER try to pick up more than 2 characters, 3 at the very most. I mean sure feel free to mess around with more, but don’t put the time into actually learning more than 2-3. It’s impossible to learn how to play a ton of characters at a top tier level, the less you play generally the better you’ll be because you understand that character better than somebody who spreads their time out.
So I vote continue with Rog, and pick up a different character to complement his playstyle. Personally I play Rog and Akuma, although there are definitely better alts as far as covering the counter-picking bases go, I just really like Akuma. It’s best to choose an alt for Rog that doesn’t need to be really close to do damage, since Rog is already useless outside of close-mid range. I’d go with anything but a rushdown (i.e. Viper, Rufus, etc.) or a grappler (Gief, Hawk, Hakan, even Abel), so that really leaves you with zoning characters (Ryu, Sagat, Gouken, Juri, Guile, Deejay, and to a lesser extent Akuma/Ken).