3rd base is the biggest spot to try and improve. The only issue is the options aren't great. Jung? Bad defense and the Rangers might not be selling. Chapman? No trade clause, bad contract and Savant page is kinda ugly. Paredes? Not great defense and his profile isn't ideal for Am Fam. Casey Schmitt was someone I advocated for before. His Savant page looks promising but this season feels fluky. He is only playing the outfield because of Chapman and he stinks there, completely playing out of position. His bat is playing much better outside of Oracle.
Perhaps you get someone and move them to 3rd which is risky midseason. CJ Abrams would be interesting but would cost a lot. You could kick the tires again on Ketel Marte if the Diamonbacks sell. Gunnar Henderson would be interesting but I don't think the O's would entertain trading him.
So then maybe you look at the outfield. Buxton would be the ideal target but he has a no trade clause and sounds like he doesn't want to leave. Not sure what happened to Jurran Duran but he is playing poorly. At this point, I think you ride with what you have. Call up Lara at some point and move Mitchell to right. We need to get positive production from that 3rd outfield spot. You can also continue to get Bauers some starts in the outfield with the Miz and Harrison are starting.
Starting pitching is a popular pick for improvement. Joe Ryan is a guy that is often in rumors. He is pretty consistent and I like that he is under control for next season. He would definitely be a playoff starter which I think is a requirement at this point. Logan Webb is another guy. He is under contract at a somewhat reasonable price for a few seasons. We saw firsthand when he dominated us. I think the Giants will prefer to shed some salary. It is unlikely they can move Chapman, Adames or Devers so this may be an opportunity. Freddy Peralta is another guy you keep hearing about. I would pass on him for this season. I'm not including Skubal because I think the price would be too high for the risk you are taking. There are other starters available such as Sonny Gray but I just think it might be a stretch for the Sox to trade with us again this quickly. (maybe I am wrong with that)
When you look at the Brewers 4-6 starters, you can make the argument that there just aren't a lot of major upgrades out there. (at least in the realm that you want to give up multiple top 10 prospects) This is a good thing obviously. The only concern is that you want to protect these young starters a bit on the innings total.
Conclusion: Brewers call up Luis Lara and send out Blake Perkins. They trade for Casey Schmitt from the Giants and put him back at 3rd base where he belongs. You're taking a chance that this is a career year from him. It is not in the Brewer's recent history to trade major prospects for "name" pitching so I think we stand pat on starters and maybe trade for some random reliever.