How do I wash multiple baseball hats at the same time?

put them in the top portion of a dishwasher

Put them in the top rack of your dishwasher. http://www.wikihow.com/Clean-Baseball-Hats-with-a-Dishwasher

I put mine in the dishwasher. I know it may sound gross, but I found the idea on CNET

Here are a couple of links on other ways to wash, since the dishwasher can shrink them, or discolor, or misshape them:

http://www.artofmanliness.com/2016/09/08/how-to-clean-a-baseball-cap/

https://www.thespruce.com/how-to-clean-baseball-caps-2146344

Sorry, I'm back. I've been researching this to wash my hubby's caps for some time, haven't done it yet, but I also found this one about doing the dishwasher, but using borax instead of dish detergent, I may give this a go:

http://tiphero.com/clean-baseball-caps/

We purchased several baseball hat frames - example attached in link - and wash in washing machine on gentle cycle. Prior to that, I washed by hand, as I refuse to put the grimey, sweaty caps in the dishwasher where we place dishes that we eat on. Just grosses me out too much. Then just let air dry.

https://www.walmart.com/ip/Cap-Washer/132546727?wmlspartner=wlpa&selectedSellerId=4040&adid=22222222227072948313&wmlspartner=wmtlabs&wl0=&wl1=g&wl2=t&wl3=184882355704&wl4=aud-310687321802:pla-289918247236&wl5=9031180&wl6=&wl7=&wl8=&wl9=pla&wl10=117430533&wl11=online&wl12=132546727&wl13=&veh=sem

Top rack of the dishwasher .

I have a front loading washer, and toss them into net bags I use for delicates and wash them with towels. I dry them over a pan or large container with the right shape. They dry fairly quickly and looks so much better. I use HE detergent pods and Oxyclean pods.