When you look through the file you will see:

--types of mercs that are available in each region set
--max number that will become available in that region set
--probability of a each merc unit becoming available at any given time in that region set

If I pick up some mercs in one province in one of the regions, it depletes the pool for the rest of the region that turn. So often I find that there are fewer mercs than I though in a given area. In your example if you take the three EI units available then you probably will not have any available in the next adjacent region (unless it is in a different pool.)

Strategy tip: When invading or being invaded, snap up those mercs if you can. It is not so much that they will help you, as that you can deny the AI extra troops. For example. If you invade an AI land and see that you have 10 good units and the AI has 6 and you will reach their city, it sounds like an easy win. But if you also see 4 units of mercs available, what will usually happen is that the AI will buy them, boosting its forces. It will probably also produce a unit, and perhaps have a couple appear that you couldn't see. So the small AI force often will outnumber you considerably by the time you engage. The AI is smart about buying mercs. When I know an AI army is coming into my lands, I deplete the merc pool before it arrives. When you consider it, this is a rather historic aspect to the game. Buying loyalty and forces in the face of an invasion or when conducting one was a very important facet of classical warfare.