"Homemade" reference measurements may be tricky and will entirely depend on what your instrument measures.
The main instrument I use is the Lambda 1050 UV/Vis/NIR Spectrophotometer which makes a reference run with a white target of known reflectivity prior to any measurement.
https://www.perkinelmer.com/product/lambda-1050-2d-base-inst-no-sw-l6020055
This measurement essentially gives a known value measured by the spectrophotometer in order to have a 0-100% dynamic range. Otherwise, if the reference measurement is not run, you run the risk of measuring transmittance or reflectance of >100% (which for most real materials is not possible).
So the actual reflectance curve of Aluminium is R_Al_true = R_Al_meas * R_Al_ref ?
Not strictly necessarily, unless the instruments with which both measurements are made are exactly the same (which is never the case).
If the only reference you have is the aluminum mirror it should be fine for some wavelengths, but in general a calibration run should be done with a white reflectance target, such as this:
https://www.edmundoptics.com/f/white-balance-reflectance-targets/13169/
(This is on the expensive side, your spectrophotometer may also have its own white diffuse reflectance target):
Here you can see the reflectance spectrum for a relatively inexpensive aluminum mirror:
I think that maybe if you multiply the reflectance spectra you would have a time-domain convolution which may not be necessarily what you are trying to achieve here, since the reflectance spectra multiplied by a reference may not be what you are trying to achieve here.
These comments are of course assuming that there is no calibration run in your instrument (which is unlikely but it could be the case). In the case where you have no reference of what 100% reflectance is, then it makes sense to calibrate the instrument first, but multiplying a reference spectrum is not something that I would assume would yield a useful measurement.