September 1 allows the Twins to add two players, but there are a lot of players that could/should be available by that date. Alcalá, Gordon, Paddack and Miranda have all been out quite a while (Paddack and Gordon are on the 60-day IL). Miranda was optioned once this year, so an option to St. Paul would be pretty painless. Gordon doesn't have any options remaining, so if he goes on rehab he would have to be activated or DFAed. Space would have to be cleared to add back Gordon or Paddack.
Meanwhile Kirilloff and Buxton could be ready to be activated this month or early in September. Ryan's 15 days are up in less than a week, so all of them could be back. Lewis is set to be activated on Tuesday.
I think Keuchel's days are numbered, but the position player crunch is severe. It would be on brand for the '23 Twins to DFA Gallo after he reached base on five consecutive plate appearances, including two homers.
Usually, new injuries make space. Solano and Kepler both played today, so it doesn't look like either of them will go on the IL. Castro might end up on the IL due to his back issues and perhaps it will be determined that Correa would benefit from a minimum stay on the Injured List.
The future transactions will be fascinating.