Well apparently it is possible, and it has been done, probably more than once.

In his German language podcast Dr. Drosten, a Coronavirus specialist from Charite Berlin, is addressing this exact issue.
In case you have never heard of him, his lab was the first to publish a working PCR test protocol for SARS-CoV-2 back in January 2020 [1]

Here is an DeepL translated excerpt from the transcript for his latest podcast [2]

"The whole thing has a certain complication. The Ct values that we have here are not easily comparable between the individual test manufacturers. Basically, you can say that a high Ct value always indicates a low viral load. And if the Ct value then becomes lower, then that also becomes a higher viral load. But we can only compare them numerically as long as we are in the same test system. The differences there are sometimes considerable. There are test manufacturers where a value of, let's say, 25 is nothing at all worrying, while the same value of 25 in another manufacturer's test shows that this is already a seriously infectious concentration. This is simply because these test manufacturers do not standardize on the Ct value. That would not make sense either. Instead, it makes sense to simply determine what lies behind the Ct values, namely the actual viral load. You can do that, you have to calibrate that."

and further

"We did that in the fall. All the laboratory work that is necessary for this was done in September and October. I had already explained that to the public in the summer, how that works. We worked in the lab to make this possible. We have also come so far that viral load standards... You really have to imagine it as a small plastic vial with a test solution in it. It contains killed virus of a known, defined concentration. You can order it in two or three defined concentrations from a company that sells such a thing. The purpose of this company is to provide quality assurance for laboratories and to offer the necessary calibration standards. And these calibration standards are produced here in our laboratory, this killed and exactly quantified virus. So we have produced this calibration standard. We have also developed instructions, which are then recommended by the Robert Koch Institute, on how the laboratories can use this calibration standard to convert their Ct values into viral load ranges, which either actually lead to an exact viral load or which - and this is our recommendation - lead to assessment ranges. And that is to an assessment of highly infectious, low infectious, and borderline. So roughly speaking, that is expressed a little bit more genteel and precise. There's even a recommendation on how to express that on the medical findings then. Medical laboratories can do all that. This is also done in practice in the hospital sector.
routinely used for discharge decisions. For example, a patient is in the intensive care unit. He is getting better. He should be transferred to a normal ward. Now the question is: Can we do that? Is he still highly infectious? Then a quantitative PCR test is carried out with these findings."

[1] https://www.eurosurveillance.org/content/10.2807/1560-7917.E...
[2] https://www.ndr.de/nachrichten/info/coronaskript306.pdf