ASP.net: Can I have 2 different versions of the same dll / assembly library in the bin folder?

I am working on a large web application implemented in ASP.net. The main part of the application, most of which is implemented by a third party, is managed by others, so I can not control it.

I implemented 8 custom ASP.net controls that are compiled to separate DLLs and placed in the bin folder of the application. These controls should link to multiple DLLs (or should they be assemblies?) From the main application, which are also stored in the bin folder. Name them MainAppCore1.dlland MainAppCore2.dll. This seems to be managed .NET code.

My problem is that the main application has been updated and it looks worse regularly updated in the near future, due to problems with errors, I compiled all my controls against the original version of the DLL of the main application, so now they do not load. Obviously, I can solve this problem by recompiling all the controls with the new versions MainAppCore1.dlland MainAppCore2.dll, but I'm looking for a more reasonable way

My question is: is it possible to support 2 versions of the main application DLLs in the bin folder so that my controls work (maybe) every time the main application is updated?

I do not need to edit the file web.config, as that would be politically difficult.