What might this P-68 be doing? Right now (28 May 2020, 0910 UTC) this Partenavia P-68 is repeatedly flying, alternately, northbound and southbound over Rome, Italy, in regular straight paths about 45 km long, some 400 meters apart. Flightradar24 gives for it just the model (no callsign, not anything). Yesterday morning it was doing the same, for at least six or seven runs.

What might it be doing? Is this the same kind of flight as in this other question? I can't say, since the flight pattern is somewhat differen: for one, the parallel paths there are some 4-5 km apart, while in this case they are less than 0.5 km.
According to the pattern and altitude, this aircraft is probably doing aerial photography or 3D mapping (or both !) for services like Google Maps or Apple Plans.
The Partenavia P-68 Observer is actually made for this kind of missions. According to this link, the Italian State Police uses it too.  

Since it's happening over Rome, it could be on an archeological mission too, but that is speculation.