Yes, I think this puzzle is far from solved..
The front is certainly the same as quite a few Aprilias from the mid to late 1940s but the rest of the car is strange.
It might indeed be an Astura as FrontMan suggests, maybe with the first example of this nose; the car aft of the nose certainly looks much less neat and resolved than the later (?) Aprilias.
And the four headlights? Was it like that when first built or is that a later alteration? The earliest example of dual headlights I have found is the 1949 Pininfarina Alfa 6C 2500 SS in Corrado Lopresto's collection, but if the puzzle car had those from the off it may be the very first example of such headlights.
The truth must be out there but so far I have found nothing that resembles this car apart from the nose.