Running a .net 4.0 application under a 2.0 site in IIS

I have an IIS "site" set up with an app pool that uses .net 2.0. I have added a .NET "application" to the site that requires .net 4.0.

I set the app pool for that specific site to use .net 4.0 but when I do I get a 500 error with Error Code: 0x800700c1

Can I do this? Or am I trying to do the impossible?

Notes: I wanted to refrain from changing the app pool of the whole IIS site to use .NET 4.0 because there is a LOT of code to be tested if I do. I also can't add it as a separate site entirely because I run into cross origin issues.

Update: Even if I set up both app pool under .NET 4 I get the same error. I have to use the SAME app pool for both the site and the sub-app. I feel like this should not be a requirement.

I changed Enable 32-Bit Applications to True for the application pool for the .NET 4 sub-app and it worked while keeping the parent site with an app pool of .NET 2.

Haven't completely tested it, but so far it works.