These are called double hybrid functionals. You add a fraction of MP2 correlation on top of the DFT energy.
A good reference is e.g. the review by Goerigk and Grimme from 2014 published in WIREs 4, 576 (2014). Note that this is already 7 years old; many double hybrids have appeared since then. However, it should give you a good overview.
Susi is right that these are called double hybrids, I'll just add a bit more to complement that correct answer. My answer to "What are some recent developments in density functional theory?" was about double hybrids, and it looks like the community here considered that to be one of the most important "recent" developments in DFT.
There are a number of open-source and commercial software that can do a completely random substitution alloy.
In the open-source segment, you can try the python software: Pymatgen (https://pymatgen.org/). Atomsk (https://atomsk.univ-lille.fr/) is another great software to do this. I have tried to do this using Atomsk and it works perfectly.
In the commercial ...