2. Spurs move up to 17th by consolidating picks to Houston
The Houston Rockets own the third and 17th picks and while the Spurs should first try to trade up to three, they may instead focus on acquiring the 17th pick. Trading 20 and 25 to do so might seem like an overpay for the Spurs, but they could have good reason for such a move.
The Spurs could pursue Zack LaVine, Deandre Ayton, or Collin Sexton in free agency and, if they do, it would indicate that the team is trying to accelerate their rebuild. That means that the Spurs would have little use for four rookies and could do a two-for-one deal for a pick in the teens for that reason.
In fact, the Spurs could easily end up with a player that was projected to be selected ninth with the 17th pick because of the uncertainty surrounding the back half of the lottery. That could make it worth dealing an additional first to move up three spots. Meanwhile, the Rockets are still early on in their rebuild, and having the third, 20th, and 25th pick would certainly help.
If San Antonio wants to move up even higher in the NBA Draft, they could make a 3-for-1 offer for a top-five pick, which I'll explore next.