With some serious digging, you'll find a solution. There are lots of square ones like oldoak2000 posted.
The self sealing one down the page on this site is 3 3/8". It is designed to go on first, then you put the regular one over it:https://www.plumbingsupply.com/escutch.html#selfseal
Also google "smitty plate" for some possible ideas.
You could buy a 4" cover plate and drill the center out: https://www.ferguson.com/product/proflo-...75?skuId=337175
Googling "shower head Escutcheons & Cover Plates - Plumbing" comes up with hundreds of images/links