In reply to tizer:
Ones I've done:-
You can do an overnight on the Sella massif - we went up VF Brigadata Tridentina, stayed in Sella hut, then down VF Vallon and up VF Piz Da Lech the next day. Near Cortina you can go up VF Rene Da Pol and stay in the Cristallo hut, then descend the VF Ivano Dibona the next day, fitting in the short Cristallo summit one on whichever day you have time.
One I've done parts of:-
In the Brenta you could go up the Groste cable car and do VF Bernini & SOSAT one day to Rif Alimonta, then VF Fellice Spellini & Oswaldo Orsi the next and stay in the Tuckett hut, then VF Bochette Alte/Centrale on the third day. There's more VF off the ends of that area where you could add a couple of days onto your tour.
Dunno anywhere where you'd get more days pure VF than that without going down to pass or valley level. In Austria you could look at the Lechtaler Hohenweg - more high walking than VF, but you could do 8 days.
Post edited at 23:01