If you mean two objects where the first has a singularity and the second "just" an equivalently heavy matter-object, strictly speaking in classical GR (as the o

If you mean two objects where the first has a singularity and the second "just" an equivalently heavy matter-object, strictly speaking in classical GR (as the only agreed-on current theory) the latter will invariably collapse into the former so the answer is no. But on the other hand, I don't think any modern particle physicist actually believes there is a singularity as its a purely classical construct. This is why there is so much research into black hole information processing in the first place.