Digitally signing a strong named .NET assembly

I have a .NET assembly which I've strongly named, to put it in the GAC. However, the same assembly is also digitally signed using a .pfx file later on, for digital signature.
I've noticed that this assembly, which has been so dual signed, fails the strong name validation, and does not install in the target machine's GAC.

Could it be possible that the digital signing procedure removes the SN-key generated strong naming procedure?

The digital signature is essential and if the 2 are not compatible, then can the file be signed by the .pfx file instead, as easily as the SN-naming process?

Also, the assembly is in C++/CLI, not in C#.