My recommendation is to have a request to play against option. I feel like this solves so many problems with toxicity. You have a toxic person queuing up with someone for 3 games straight. That's so dumb. If I have someone that is super toxic who I've already reported I shouldn't have to play with them over and over until I abandon and get penalized. If you have a request to play against then it will queue you up against that person more often. It also really confirms the mmr system. It says OK valve, if you think this other player is as good as me I want to play them as much as I can. I certainly believe this will help solve a lot of problems with a simple button and algorithm.
It solves:
-Separating feuding players that ruin games for 3 other people and themselves.
-It is an insurance policy on the MMR system that can not be argued with.
-It heightens competitiveness and allows for a whole new rivalry system that is much healthier than forcing 2 people that hate each other to try to "work together."
-It will make people re-queue so they can find the person they want to play against so much.
-It gives players peace of mind that they will be less likely to see a person that ruins games or is abusive.
-For individual occurrences it would be much faster than the report system.
-It will really pinpoint the most toxic of players much more than the report system.

In closing I think the peace of mind it will give a player that feels either cheated by getting by mmr system, or a game-thrower, or a racist, or a sexist, or anything and anyone, is something the community is looking for. And if the entire dota community wants to play against certain people, valve and steam will know who are really causing problems. It offers short term and long term solutions. Please add any ideas I might have missed. Thank you.