I am renovating a house with a mishmash of electrical circuits and wiring. I am able to gut everything and start over in some of it, but there are outlets and lights that will remain, mostly in bedrooms. There are very few grounded circuits. I can find info that says I can't extend an existing ungrounded circuit, which makes sense. I can find nothing that tells me I can't run a new, grounded circuit and connect to ungrounded wire and outlets. As long as the wire size is appropriate, it seems that it's safer than it was before, but maybe the NEC doesn't see it that way?