Anyone know how to get multiple Protonmail free tier accounts on an android phone?

They are a great company and are worth supporting in my opinion, they do care about privacy, are based in Switzerland of which was chosen as the location for its strong privacy laws and commitment to protecting user data.

Edit: they just emailed me announcing that they have a 40% end of year sale right now. (absolutely not affiliated)

I wish they could just sell email addresses for those that are hard up for money, but for me, I ended up paying for the mid-tier package for aforementioned reasons.

I guess a web app manager like native a would work but I suggest paying for an account.

I support what the others say, it's cool if you can pay, but it's not a must IMO. If you're fine with the base tier, or can't/don't want to pay for more, there's no shame in that.
Shelter works fine to keep two accounts, which should be enough hopefully, otherwise you will have to use the web client.
There was an experimental app that allowed you to have a potentially unlimited number of duplicate apps (twoyi), but it's sadly discontinued, there's also another called MultiApp, but there's something yiffy about it I can't quite put into words

Download the ProtonMail apk from a trusted place such as APKMirror, and then use Revanced Manager to change the package name. Install the patched app and profit! You can do this over and over again.