Premades should be hit with matchmaking penalties like Duos used to be in the old system.
The old system hit you with an effective 'penalty' to make up for A) Communication B) Consistent synergy C) The possibility of a high MMR player giving an advantage to a low MMR player. These are all completely reasonable, and that penalty should not have been removed.
More players=bigger penalties. Premades get normal MMR gains/losses based on their group MMR (after adjustment).
The solo players get LP/MMR gains based on the MMR of each individual player, including the premades. Because the premade players are lower than their adjusted group MMR, this makes it so solos are rewarded for winning with low MMR players and not punished for losing with them as a result of the system.
Best part? **It encourages more cooperation between solos and premades because the SOLO players are rewarded for winning with that premade.**
It goes the other way as well. The solo players could be considered 'mentors' of sorts in nearly every case (except high elo smurfs). This means the premade **should** be a little more likely to cooperate with the solo.
It still wouldn't be a perfect system, but it'd be a huge improvement over what we have now, especially since it'd make boosting a little harder.
If you have any suggestions, please voice them below. :)