Yes there is something that you can try, The Insert is fitted in a way similar to a rivet, in that it is compressed from the inside of the tube against the inside diameter of the frame.
You can try screwing a longer (steel) bottle cage bolt and steel washer 10mm into the thread,hold the bolt securely, and then turn the nut carefully down onto the frame/washer until it starts to grip/pull against the softer/threaded insert.
You should be able to apply enough force onto the nut to take up the free play in the Insert but do be aware this is a very small amount, and the Insert itself is easy to damage.
If its fubard completely you may need to drill the Insert out and replace,Theres a company called WURTH that make quality replacements with a ribbed edge,these are particularly suitable for bike frame applications as they are zinc coated,will not rust, and once fitted correctly won’t move,The downside is you will need to remove the BB or headset to get the swarf debris out.
The proper ” Nutsert” tool will set you back £40 quid so its probably worth contacting a local car body shop or garage to help you out..HTH 😉