I was just fine-tuning the intonation on my 2010 Amcn Standard Strat and have a question. The electronic tuner shows all strings (open) in tune, all 12th fret harmonics in tune, and all fretted notes in tune -- except the low E string, which is slightly sharp at the 12th fret. I've got the saddle adjusted as far back as it will go. The strings are new and I've stretched them.

The wee bit that the string is out is not noticeable (to me, anyway) so I'm not concerned about taking further action, but for curiosity's sake, what would be the next step -- adjusting the height of the bridge plate?

You could remove the spring behind the saddle. It will give you room to adjust the saddle further back.

cheers, Serge

Are you sure your neck have not too much curve ?
If yes put it "straight" this will helep for you saddle.

If curve is ok, micro tilt adj needed : turn clockwise the allen ( look how to do these adjustments on fender.com).
Whith this adjustment, scale will be longer and you should adjust your saddle.
But you have to lower all saddle and do all of intonation.

Don't forget almost all tuner except Peterson Stroboscopic have big error for intonation.

+1 on checking your neck relief. I have seen this before, but it is almost always a setup issue like too much relief or improper neck pitch / angle. Don't think I ever seen a Fender where the bridge was not located properly. Removing the spring, as stated above, may help give you that extra bit of adjustment, but check you neck relief, and if it is good, you may need to use the micro-tilt feature, and tilt the neck back a tiny bit. Just be sure that if you use the micro-tilt, loosen the 2 screws on each side of the micro-tilt hole first so the neck can tilt when you turn the micro-tilt screw! And you want to tighten this screw.....to tilt the neck back.....but NOT MUCH. Maybe not even a half to full turn. That will cause you to have to setup the guitar again too, but you may find there is plenty of room for adjustment after this. If in doubt.....go slow with micro amounts of adjustment.....or pay the repair shop to do this for you.

Are you sure that your bridge-tremolo have the right angle ? If the springs are too loose, the scale of the guitar will be too short