Behr makes a one part epoxy paint.

http://www.behr.com/consumer/products/floor-coatings-sealers-and-prep/behr-premium-one-part-epoxy-concrete-and-garage-floor-paint

If using the Behr One Part Epoxy on the bare concrete, be sure to use their bonding agent first. The One Part epoxy will stick directly to an existing sound finish. Make sure it is clean and dull it down if it is a high gloss enamel.

Usually the only concern is adhesion of one paint to another. Like all projects, the PREPARATION is KEY. If you miss a step you will get bubbling and peeling. The same is true for the old exposed concrete.

You will have to find out what type of cleaners have been used and how to get rid of them (known as contamination) without removing the existing paint (ahhhh....there in lies the rub).

I would start with a test patch over BOTH surfaces. Clean-up/prepare a 2ft x 2ft section of concrete over both concrete slabs. Do ALL the techniques you NEED to do to get this stuff clean (sweep, mop, dry-vac, mop, dry-vac, mop, dry-vac, etc) until you feel the section is as clean as possible.

Then use a primer/bonding agent over that area (regardless of the surface) and then use the epoxy paint. Wait for 2-4 weeks (yes....WEEKS) to see if there are any issues.

Is this a suspended slab (like a 5th story apartment) or is the ground level?

You need to add some non-skid to the mix. They sell pumice for this. Without non-skid additive the floor will very slippery when wet.

Unless wetting of the floor is anticipated, the urethane will be no more slippery than other type glossy floor finishes. Any floor is more slippery when wet. Adding grit will be regretted every time it is necessary to scrub and mop the floor. It will tear apart sponge mops and squeegees.