The only legitimate (but still morally ambiguous) method you could use would be if you made a spare, "throwaway” account to follow it on and snoop on it with.

However, people with private accounts may be suspicious if an unused account tries to follow them - and they may even go as far as to check post dates to see how old the account is if you're going the ‘full hog’ to set up a fake. It really depends how invested you are in it all.

I’d advise to leave a private account alone - theybare private, after all, and if they don't want you following them, they probably have a reason for doing so.