What are the possible upgrades for a 40-year-old Bottecchia 10 Speed?
Bottechia frames from that period use an italian threaded bottom bracket. I assume also down tube friction shifters? 

The simple answer is that you can upgrade the bike all the way to current standards, if you are willing to spend the money. But it is not what most would consider to be cost effective to do so.

Upgrading the rear freewheel beyond a 7 speed cluster isn't likely to work, without new wheels, and if you only upgrade to a 7-speed freewheel, you will need to change your chain to match. Changing your chain requires changing your derailleurs, both of them, preferably, although you might get away with leaving the front derailleur.

If you spend the money to go that far, a whole new bike kit, which should be possible to make work on the frame, isn't that different in price, depending on your choices. A SRAM Apex Kit should cost around $1500 dollars, including new basic wheels, and current standard wide range gearing.

But if you want to keep the original wheels, you will be very limited in how far you can change things.