Is there Airframe Life extensions by request?

If you're speaking of going beyond the limit of a life-limited component (like the 12,000-hour limit on the Grumman AA-5-series Traveler/Cheetah/Tiger center spar), it's theoretically possible, but a practical impossibility.  It would cost far more than your plane is worth to get the all the data and do all the non-destructive testing of actual high-time articles necessary.

I think that answers the question. I was considering purchasing an older aircraft and fully restoring it. But if that restoration doesn't extend the life of the airframe, i'm not going to bother with it.

Now that I think about it, is it meaningful to perform metallurgy testing along with re-riveting and structural enhancements?

Thanks for the feedback

Out of curiosity, what aircraft are you considering?  While I know many light planes which have some limited life components (like the Grumman AA-5-series wing spars), replacement parts are often available, allowing you to replace the affected part and then keep flying the plane.  This usually isn't cheap, so Grumman folks, for example, aren't likely to do it for a plane they're going to buy, but may for a plane they've had a long time with a lot of money invested in improvements and modifications.  So you might still have some options short of trying to extend an FAA-mandated life limit on one particular component.

The extension of airframe life would have to be done by replacing the parts with new ones as previously mentioned or by modification (STC). There are a few of those out there - I recall one for the Piper Tomahawk spar caps - lots of testing, analysis, engineering, etc. External spar cap doublers to add hours. For a particular make and model I would consult with the owners groups. Good Luck.