10 days is a good amount of time, assuming 2 days each way that leaves you six days, and personally I would be tempted to spend a couple of nights somewhere else either on the way, or another location in the Alps.
You can do all 5 of the famous passes with a couple of nice excusrions up dead end roads in a (admittedly busy) day;
Number 9 is not the best detour (IMHO) pretty enough, but the other two are prettier, and the restuarant at the end of it is ££££, the Restuarant at the end of Panoramastrasse Oberaar was very reasonable last time we were there in 2018, a lot can change in that time however, and the accomodation was also pretty cheap by local standards (but you are really out of the way!)
I think there is 3 good full days riding out of Andermatt, assuming good weather (it is not always good) so having 5-6 days there does leave you some wiggle room, but I would look to have maybe 4 days there, leaving you 3 each way out and back, or blast in two and free up 2 days somewhere else? or 3 out two back etc leaving an extra night somewhere....
I would consider couple ofthings:
Either a longer run out and back stopping in Luxembourg / Black Forest / Vosges, maybe for 2 nights somewhere
Or add this in:-
A stunning 7 pass run around Mont Blanc:
* 2-3 Days to somewhere on that looping ride out.
* 1-2 days to ride that loop and maybe a lazy day, or another ride out if stopping for 2 full days?
* 1 day to Andermatt
* 3-4 days around Andermatt
* 2-3 days to blast home
The options are endless, I have some mates that almost refuse to stay in the same Hotel 2 nights on the trot, I prefer a mix of moving on and having 2-3 days in one place, in 2010 we did 2 nights near Martigny (avoid the town, we were in tiny village nearby) and rode that mont blanc loop, moved onto Andermatt for 3 nights, and then had 2 nights in the black Forest on the way home (and a day off the bikes in the Spa's of Baden Baden) - all in a ten day trip, self employed back then, these days (if it were not for pesky kids!) I would go for 11-12 days rather than 9 or 10 just to have a more leisurely 3 days each way and a few days in two locations, or go the full 2 weeks off work and 15/16 days and add a third location.