How to run a third party application install using a domain account instead of the default "System" account in SCCM?

The only option i see is that you configure a script or batch file in the program command line which executes the application install with the domain admin rights.

runas /user:<domain>\<domainadmin> setup.exe

But in this case you have to pass the credentials in clear text, and this isn't really recommended. Further the password in the clear text file will remain some time in the client cache.

What's the reason for your needs?

We have a custom app that needs to be deployed to a couple thousand computers. If you import the msi file like any other msi and run the Per-System Unattended the "System" account doesn't seem to have the rights to register the libraries needed. I personally think the developer needs to correct the issue on their end but I was just looking for a work around and having a clear text password floating around the network would not be too good from my job standpoint.

Thanks for helping me clear the issue up and reconfirming that the developers need to go back to work.