I'm replacing a sonicwall/sonicwall site-to-site VPN with a mikrotik/sonicwall solution. I've done this many times without issue where the sonicwall only had one private subnet for me to deal with.

I'm currently trying to connect to a site with a sonicwall that has three private subnets that need to be passed through. On the mikrotik side, I've attempted to add additional IPSEC policies per additional private subnet, but I never get a proper connection.

To make sure I set things up properly for single subnet, I disabled the additional IPSEC policies on the mikrotik and change the sonicwall to only pass one subnet. That worked.

What special modifications need to be made to allow my mikrotik to accept SAs for the multiple private subnets from the sonicwall?

Try make the policies level to 'unique' instead of 'require'

I've tried using unique but still no luck.
I've also attempted to create individual IPSEC policies on the Sonicwall, one per private subnet. When I attempt to add the second policy (all settings the same except the local private subnet), the Sonicwall says that policy conflicts with the previous one due to it having the same remote subnet.