I mistakenly purchased Minwax Super Fast-Drying Polyurethane for Floors in the satin finish rather than the semi-gloss for my hardwood floors. I also purchased some gloss finish Minwax Super Fast-Drying Polyurethane. Is it possible to somehow combine the two products in order to get a less "flat" finish than is possible with the satin alone. Of course, I would have to figure out the correct proportions in order to match the existing finish of my floors. You see, I am attempting to "renew" parts of the floors that are worn by use and not the whole floor. I realize their is also the question of applying the new polyurethane so that the outer edges are on a gradient in order to blend with the existing floor finish.
Can this be done?

"Refreshing" a floor is a good idea so you can protect your investment. The floor should look good and also be easy to clean. With wear a poly floor will get scratches that even they are minor will harbor dirt, so it will change color.
I mix gloss and matte to get both semi-gloss and satin floor finish. You need to test the mixture so you can compare after the finish has dried.
Even though you may have used a "semi-gloss" right out of the can there can be lots of reasons why the same level of shine does not match. This is why I always mix all the cans of finish together on a large job, after stirring, and then strain.
Walking in stocking feet will polish off some of the satining agent making traffic areas shinier than edges of the floor.
You will be able to see where the finish coating starts and stops. Unless the whole room is coated you will notice a difference in sheen levels.
The difference in shine may even out with time, but you will be able to see the
renewed area.

Thank you for this information. It's exactly what I have done: mixed Minwax Gloss and Satin finishes in almost 1:1 proportion and it's pretty close to the original, twenty-year-old floor. Before applying, I had sanded done the worst areas with 80 grit sandpaper with a mouse sander and then sanded a larger area with 220 grit in order to "even out" the surface sheen. After three coats, it looks pretty good although I intend to re-sand with 220 or 300 grit paper and apply a fourth coat over a larger area sometime later this summer. Just a question of evening out the surface.
In the meantime, how should I clean the floor? I know Minwax produces a cleaner, but I read somewhere that a 1:30 solution of vinegar and water could be used. What do you think?

The easy thing to clean a floor is warm or even hot water to dissolve the soil.
The new type of low suds detergent have something that help water dissolve the soil quicker and still evaporates completely without leaving a residue.
The vinegar helps dissolve more difficult types of dirt and may help not to leave a spot with hard water, but still leaves no residue. Vinegar is also a disinfectant, so the floor will be "cleaner". Don't flood the floor when cleaning, so a mop and bucket won't work.
If you have a squeeze mop, put some old terry cloth, like a piece of a towel, under the mop so when you press down on a spot to scrub, the extra water will be absorbed by the towel instead of draining into the cracks.