There's not that many people in categories like that though are there? And even so I'd argue that yes, they're still working class, or maybe some part of the middle class, but either way it doesn't matter massively, they still don't have the power in society and don't own the means of production (ignoring for the moment the bit about 2nd and 3rd houses and assuming they're not a landlord). I accept this can get much more complicated in terms of struggle, and where they align themselves when it comes to battles over material conditions though, and that's impacted by what they have to lose in part, but plenty of working class people also will have that contradiction/conflict depending on what's going on and their own politics/position/background etc.
But anyway... surely the point is that this is a category and a category that's tied to explaining how society under capitalism operates, it's not about seeking to put every single individual in a clearly agreed box depending on their exact financial situation? Capital loves discussions like the above, it gets everyone complicit and confused in who runs and makes profit from the way the world is, whereas at the level where it really matters it's pretty simple surely?