Using static classes (or perhaps 'hardcoded' config access) is a generally bad idea. Thats why we invented "instances" - same code, but different data (e.g. different connection string).

It is possible to use different versions of a packages using the Aliases="Alias1" parameter (perhaps even using the same version???). However if there is a hardcoded access to some config-file/settings - you still will read the same config. So you should have same DbContext instances that receives different config-values and will provide access to different DBs.