I was thinking about Marcus Ogren's "Fusion Voting on STAR Ballots" proposal, which replaces the traditional party endorsements listed under candidate names with the ratings parties officially recommend giving the candidate. Two Republicans may run, one with a 5, one with a 4 from the GOP. A voter may consider herself a moderate and give higher scores to a candidate who receives 2s from both of the duopoly parties. This set-up allows voters to think of themselves as members of a particular party, but in a way that defines relative position within and between parties - "I'm an X-Y Coalition voter. I am chiefly X, but still give great consideration to endorsements from party Y".

I realized mulling this over that, with this set-up, the parties effectively submit their own ballot! We can compare their scores directly to the voters and their factional score-clusters. Could this be used to generate a kind of Mixed Member Proportional-like system that supplements single-winner STAR district results automatically, where:
(1) Voters are grouped by score-proximate party, relative to which party's ballot their scoring most resembles
(2) "Party group" proportions are compared against the party membership (or party membership weighted by endorsements) of the winners, identifying the least represented
(3) Highest scoring unelected candidates from the parties of underrepresented party-groups are seated at-large until a desired proportionality threshold is reached

(3) seems to result in candidates from 'parties that score similar to large clusters of voters that generally don't succeed in electing local winners' experiencing a strong incentive to be the most likeable candidate in their party to the general electorate, which could be beneficial given traditional concerns with PR. Another consequence is that this might result in reverse-engineering parties from unorganized factions. Identify a similarly voting, relatively unrepresented "natural party" in the electorate, and endorse according to their representative ballot (if candidates accept those endorsements). Run a couple likeable, high-name recognition candidates and you'll bypass much of the slower party-formation difficulties straight into representation, which could make parties more dynamic and incentivize 'constituent-seeking,' or just fall to strategic exploitation.

This is half-baked but I wanted to do something with the fact that fusion endorsement essentially signals a party's own STAR vote, which probably has undertheorized usefulness in Cardinal-PR theorizing.

As a side note— are there interesting party-based proportional score proposals I should read about? Party-reliance is less of a realistic proposal in the US but given academia's partyphilia I would hope there's some sketch of what that could look like. Here's one I just thought of:

Mixed Member Proportional Rep with a Score Ballot
Pick my local rep by STAR, then score the parties out of 5
Aggregate party scores are converted into a tradeable interparty asset ("Stars")
At-large seats are "purchasable" for some n stars
Parties need to meet an "ante" of a set number of seats to take their seat, avoiding fractionalizing
Parties then negotiate between each other, trade stars in exchange for concessions and legislative promises, even smallest parties get some pull this way
Larger parties weigh allowing fringe parties to buy additional seats under their umbrella, which gives them ultimate control over renegade radicals and a larger coalition at some risk
Parallels negotiations during the formation of a government in the case of parliamentary systems, so coalition governments can deliberately seat a "neutral independent coalition figure" to lead them