I think it depends on if you mean active support or armchair support. A lot of people will armchair support other teams than the one they actively support. Sometimes this can be having an armchair glory team, but often it's for more "legitimate" reasons. Can be personal links (supporting your local club and your childhood club for example, or following a club that has family connections even if you mainly support another club), or it could be clubs that have positive links to your own club (players or managers having links for example). Could even be negative links to another club (particularly if an underdog blows a big chance for a rival team). Other reasons might just be liking the way a club plays, or does business, or it's ground, or it's fans, or it's manager.
Most of the time teams would be in different league, but it's still possible to have 2 teams in the same league, although it's likely to be a much looser support if they are in the same league as your main club. I support Norwich, but do support Leicester to an extent as I now live near Leicester and a few friends and collegues are Leicester supporters. If nothing else it's useful to know how they are doing to be able to take part in conversations. That said, when they play Norwich next year, they are just another 6 points to be taken and a chance to improve the goal difference. Hoping it doesn't come down to us and them for survial though.