I recently downloaded a 30 day trial of AI Gigapixel from topazlabs.com. This software allows you to resize your photos by up to 600%. I tried it out on a file that was 719 x 958 pixels, and produced an enlarged version that was 4314 x 5748 pixels. When I put the photos side by side on our photo club's website, I and the members felt that the enlarged version was better than the original! Check the 2 versions out at https://www.dropbox.com/sh/8p2j7ofqj...97z3Rcuoa?dl=0
I then decided to enlarge the 4314 x 5748 pixel version by 600% as well. It took about an hour for the software to do this (in the background). I was expecting a photo that was 34,488 pixels on the longest side but the final version was 'only' 32000 pixels. So that must be the maximum size possible. The quality was very impressive, with just a few artifacts in the blurry background. So now I have a photo that is 106" tall (or 2.7 m) at 300 dpi. And it is about 2 m wide, so printing and framing it might be a bit expensive.
Not bad from a photo that started out just a bit over 3" tall if printed at 300 dpi.
If you have a lot of small photos that need enlarging, it is worth checking out. You can try it for free for 30 days. The cost is US$100 but a friend found a 15% discount coupon.
Cheers, Rex