I would recommend finding someone who specializes in concrete faux painting/staining. Talk with them; explaining that you often/sometimes have a client or lead that requires this specialization. This job can generate reverse leads for you IF you find the right person to handle it. Your professor will be happy to know you spent a little time to do the research for him/her, and happier for you admitting this is not your expertise. They will remember you when it is time for other jobs.
I have fauxed concrete floors. If it is on HGTV, they are dying to have it in my area. But even a brand new, extremely clean concrete floor will have issues. The majority want the slab to look like a finished marble or ceramic tile floor. Just remember that stain is not as forgiving as paint - if that is what they want. The concrete will act much like wood in that some places will grab more stain than others, etc.
A basement floor that has been "lived" on and might be in a damp environment creates bigger chances of bigger issues. Oil residues, cleaner buildup and sealers, to only name a few, will make this project a JOB with a suction hose attached to your wallet.
I personally would avoid it, knowing you also have a grade attached in a sorta-kinda way.
FauxPro