Them's the rules.
Of course,
nobody has more than 2 pets in TV.
But I don't think the "Pet Police" patrol the neighborhoods, knocking on doors for pet headcount checks, etc. More 3 dogs can be obvious more so than, say, having 3 birds that are kept inside all the time. If you're out walking all 3 dogs together, for example, then you'll be easily spotted. It would probably take one of your neighbors turning you in for the infraction to come to anybody's attention.
Bill