Then will people be voting for a candidate or a party? How will it be decided which nominees a party will run?
I suppose this could be done by some kind of preference voting as well, and the person with the highest preference vote will be the first person from a particular party to win a seat based on the party's result. In this case there will only be party line voting and no split-ticket voting.
There's a lot of ways that part of the process could work. For instance, say there were a total of three senate seats at stake in an election. Each party could conduct a preferential voting primary in which three candidates would be selected. The candidate with the highest vote totally would get the first senate seat should the party win one, the second would get the second seat the party won, etc. If the party only won one seat, only the top primary candidate would become a senator.
Or we could even hold party primaries after the elections. Say in a region of three senators, the UAC won two seats and the republican won one. At that point the UAC and the republican parties could hold open primaries, in which the winners would automatically be elected to the senate.
Of course, there are many other ways this could work.