Matrid, if you still have the '06 aircooled Multistrada 1000cc, then you have something fairly comparable to the 1000cc V-Strom. Fairly similar power & torque, fuel tank capacity (20 vs 22 litres), and similar suspension travel.
Haven't ridden the Multistrada myself - but I figure the end result rather resembles the Strom, but with quicker/twitchier steering, owing to the steeper rake & shorter trail.
If you are not suffering from too much New Bike Fever, then why not buy the Multi a new front tyre [the Pirelli 120/70R17 MT 60 RS CORSA] and see how you go with that, on the gravel roads & sandy terrain (at slightly reduced tyre pressures). There might be other, semi-suitable 17-incher tyres, but I am not aware of them - other than some (rear) low-speed rated tubed dirt tyres which would have clearance & other problems.
For dirt riding, a scratched/damaged Multistrada sounds a better idea than a pristine one. Are there engine guard bars, etcetera, available for the Multi ?
Only supremely capable and/or carelessly-rich dirt riders ought to go without them.
[The Stroms have a goodly range of aftermarket protection stuff available.]
Twenty-plus years ago, I had an aircooled Duke that wasn't too bad on easy dirt roads - but that was in the days of a tall/narrow 18-incher front & stable/slow-steering front geometry.
The Multi will be a different matter in heavy, hot going - slow slogging at medium throttle in hot weather is okay with a watercooled Strom - but the Italian designers did not have slow hot sandy conditions in mind when designing the aircooled 1000. But you would probably be okay at moderate speeds & light throttle (and using a 15W-50 synthetic oil).
If you absolutely must get a new/newer bike for much dirt, then I'm thinking something "completely different" from the Multi or V-Strom would probably be the go.
A thumper with real long-travel suspension (and lighter weight) sounds the choice - if you can live with the leisurely on-road performance. Upmarket (and heavy to hoist-back-up-again) stuff like the 1000cc KTM, and 1200GS shaftie, are nice, if you can live with their reliability problems. Or maybe the 1200XTZ Yamaha or 800XC Triumph?
All in all, if the dirt itch is upon you, why not buy a cheap old Suzuki DR650 or the watercooled 400, and run it for a year : before deciding whether to continue like that - or to sell the Multi and the thumper at the same time, and get something new?