It sort of depends on how the legs are attached. If they are a mortise and tenon joint, you can disassemble the joints, add shims if needed, and re-glue. The original was probably done with hide glue, which you can still get today in a premixed, liquid, form. This will reactivate the old glue and is probably the best choice.

If there is some type of metal hardware, then you'll need to say what (but most of it can be tightened, which is obvious.)

Generally if there is a wood-to-wood joint adding a screw is not the best of ideas. A glue joint spreads the stress -- metal hardware concentrates it. I don't think I've ever seen a broken chair or table joint that did not break right at a metal fastener (screw, bolt, nail, etc.) So I'm with you there, but for a different reason:

As far as "touching," I'm afraid antiques road show has created a nation of deer in the headlights (see link). Not fixing it will accelerate its demise and make it worth nothing.

Here is a link that might be useful: Antiques Roadshow

Ok, I'll post some pics on here so you have a little better idea of what i'm looking at. I se no wood-wood joints, i see no metal hardware... i'm just not sure untill you give me your input after viewing the pics.
Give me a day or so and I'll get some pics on here.

Thank you kindly for your reply!!!

If there are no joints and no metal hardware, it's just a pile of boards. They're there, somewhere.

"The original was probably done with hide glue, which you can still get today in a premixed, liquid, form."

You can still get it in the original dry granulated form, but you need a glue pot to heat it up and keep it heated.

I still use it to restore old pieces.