Sure, Hertz, Europcar, Avis, they all do it but they will all charge you for a different drop off, especially if you rent on the French side of Basel and leave in in Rome.
Thank you for the reply. Had tried all the regular car hire sites and none of them can even offer a van let alone give a price. Was wondering if there were specialist Uhaul type of companies for people moving. Likely going to have to rethink our plans
If you’re moving it might make sense to just find a haulier who would likely combine your load with many others and also collect loads on the way back. There are a number of online platforms where you fill out your inventory and hauliers give quotes.
Just googling I found this and they seem to offer point-2-point anywhere in Europe.
And within Switzerland I’ve used Movu.ch who were pretty good, but only operate within this country.
Alternatively if you’re determined to drive, you could always pick up a van from Milan and then return it to Rome. The national one way fee will likely be a lot less than cross border.