When you think you can buy a Vax with NLOS which admittedly you'd end up having to wash the filters all the time PLUS have a 6 year guarantee slapped on it, there's a lot to be said for buying cheap.
However, if I owned that many pets I'd probably have two vacuums - one with a large dust bag capacity such as the Numatic option (or even a SEBO D2) and a bagless for every day hair removal.
But with owning dogs (and having had to put up with the ones my relatives bring when they visit and stay for months at a time) I also do a lot of steam cleaning to neutralise areas, especially carpet. Once the carpet has dried out, the amount of pet odour is LOWER than relying on dry dirt suction all of the time.