As Klem said, all finishes start off as glossy and then manufacturers add "flattening agents" to make them less glossy. It's import to thoroughly stir the can before and during use the keep the flattening agents in suspension. If you think you might need two (or more) cans for a project, it's best to combine them into a single larger container and mix them well. The same is true of paint. While modern manufacturing techniques are very good there may be some minor variations between batches.

Yes, you can go over the piece with another coat of satin following the manufacturer's directions for multiple coats to even things out.

I'd go a step further and say that all coats except the last one should be gloss. too much of the flattening agent will muddy the surface. I pretty much only use gloss then polish the surface, eg with 0000 steel wool, to achieve a matte surface.

I thought I had stirred it well, but apparently not well enough. I'll go at it again, and hopefully end up with an even matte finish on all 3 pieces.

I often do as rwiegand does in using gloss then rubbing to gloss level I want. I use finishing wax along with steel wool or scotch pads for semi to high gloss.. If you decide to rub I recommend waiting at least 3 days ( there's no limit on how long and 30 days is better than 3 days).

Stir up all that thick stuff at the bottom of the can. Those are the solids that are needed to cut the sheen down. It's always important to stir well in between as well. The cans that have been sitting on the shelf longer in the store will demonstrate greater need

I mixed, mixed, and mixed again, poured the contents of the full can into the empty one, and back again. A final coat on all and it's a nice non-dull satin. Thanks for all your help!

From the picture it looks like satin. I don't see a glossy sheen. Now satin and matte are not the same. I don't know of any clear coat that gives a matte sheen. Satin is the closest off the shelf. There is also the off chance that the product in the can is mispackaged although less likely. Did you sand in between coats?

I did sand between coats. The first (two-tone) photo was definitely glossier than the final (well-stirred) satin one.