Do hereby propose that each state be given a 3rd Senate seat. Senate terms should remain 6 years long, with an election for one of the Senators occurring every 2 years. Senator's votes should no longer be counted individually. On each issue whichever side the majority of that state's Senators agree gets the 1 state vote. This should give greater importance to each state as a whole, rather than individual voters, which is the point of the Senate to begin with.
Note: This has been stuck in my head for a couple weeks now and I wanted to try and get it out. The unlikelihood of such actually being taken up is noted. And please ignore the government growth aspect and focus on what it might mean for state's power. This is a piece purely to prompt discussion.