But that really is a function of how many people compete for those seats.

True. Maybe. Depends a bit on the party discipline. My thought was that if you can only vote for 1 person and the top four get in, you pretty much can't keep out at least one minority candidate. If the minority party runs too many candidates, they risk losing all seats. If they run just a single candidate, they're going to get one seat. If they run 2 candidates, they might not.

You could also use a form of ranked voting. Vote for 1st, 2nd, and 3rd choice. (Or more, depending on the math). Count up all the 1st choices. Eliminate the bottom vote getter, and move those votes onto the voter's second choice. Eliminate the new bottom vote getter and move those votes to the next down the line. (Could be second choice for some, 3rd choice for folks who picked the bottom two as their 1st and 2nd choice. Repeat until you have the desired number of winners. (Perhaps 4 in our example, could be just 1 in our current system of a single representative for a district.)

--Peter

PS - For a better explanation of ranked choice voting, here's a couple of good videos:
YouTube: The Voting System That Should Replace Every Election (CGP Grey) CGP Grey
YouTube: Ranked Choice Voting Explained — with Cute Pets | Robert Reich (Robert Reich) Robert Riech