Outside London, route allocation by depot / garage has tended to be less rigid, but there must be a lot of examples. Going back to the pre-NBC days, companies that had outstations, the outstation crews / drivers often didn't work Sundays so a service that had a part / whole allocation from outstation was worked from the major town end.
In London, as others have said, until the 1980s at least, a lot of routes had Saturday or Sunday allocations that were from another garage, in part at least to balance out weekend work - some suburban routes had a higher vehicle / crew requirement on Saturdays than on Monday to Friday. A few I can think of - Muswell Hill had a part Sunday only allocation on route 102 (I think the 43 didn't run on Sundays or only ran a small part of the route), Upton Park had a Saturday allocation on route 86 (off the route 15 weekday allocation, Middle Row in turn did more 15s on Saturdays, and Poplar were somewhere in the mix with a Saturday allocation on route 23 as the 40 had a heavy weekday peak.) Elmers End had a small part of the Saturday allocation on route 54 (off the route 12 rota) and the whole of the Sunday service which went OPO on Sundays only in the early 70s (Elmers End operating it on Sundays continued after the weekday service went OPO in 1978 - Elmers End's Sunday allocation later moved to route 75 and in turn to Croydon Garage when Elmers End closed.) New Cross had a Saturday RM allocation on route 89 alongside the daily RTs from Bexleyheath, Catford did the whole of route 192 on Sundays.
In the 1990s, when routes started going OPO on Sundays only, other garages would sometimes be involved - New Cross doing Sunday 36s and others have been mentioned - again to balance the amount of Sunday OPO work at each garage. Merton's Sunday (part) allocation on route 22 started like this and hung on for quite a long time after the weekday route went OPO. Similarly, some routes were midi-bus on Sundays (in an era when Sunday shopping didn't exist) and some of these were from a different garage - if I remember right, Plumstead midi buses did the 54 on Sundays for a while, for example.
And with tendered routes, there were some odd arrangements - the 19 had its weekday Routemaster allocation from (what was initially Kentish Bus) base in Battersea, but the OPO Sunday service ran from Kentish Bus Leyton, then later other garages including Grey Green Stamford Hill, Arriva Tottenham and Brixton garages.
Boxing Day (in the 1990s / early 00's) before Sunday service became standard brought some one-off allocations because some garages didn't open for the day - there were a few extremes involving Boxing Day only routes - Ensign / Capital Citybus ran an 86B on boxing day for a few years, and others included Metrobus running the 208 once or twice.