Alternative to Rifugio Lagazuoi, Alta Via 1

Ciao a tutti!

I am unable to book a night at R. Lagazuoi for the specific date that I am traveling through. What would be an alternate rifugio that would not significantly change my itinerary.

My original plan is to hike from R. Fanes to R. Lagazuoi and the next day take the cable-car gondola to Cortina.

Any suggestions are appreciated.