I think what he means is to have multiple separate units trained "at the same time" and "in the same city" although obviously not always having the same training times ... so while you are training an Uber Knight and a Peasant archer, you will likely to train almost 2 peasant archers to one Uber Knight.
In either case, I don't think its necessarily a bad idea, although it does detract from the company's uniqueness in being able to field more than one soldier at one time. However, if you made mass-unit infantry a considerable price deduction (more-so than has been previously suggested) then this proposal of having multiple units trained at roughly the same time could have some merit ... and might even have an added effect of focusing on more diverse armies.
The only penalty I could see is that, with enough stockpiled resources ... someone could train a HUGE army in a relatively small amount of time, with the only penalty being increased maintanence costs. Which might be a bad idea.
Hence, my proposal will be that once you tech "Party" you can train 2 individual units parallel, and when you tech "company" you can train 4 individual units (or two parties), parallel ... and onwards, where the tech below can train 2x parallel, and the tech below that can train 4x parallel, and the tech below that can train 6x parallel, ect.
So, assuming that unit sizes are 1, 4, 10, 100, 250, 1000 .... then once you tech legions you could train as many as 24 different individual units parallel to each other (or 12 parties) (or 8 companies) (or 4 platoons) (or 2 regiments).
In this way ... you could have the city devoted to building one legion of club peasants, or 1 company of death knights, 1 platoon of footsoldiers, and 1 regiment of club peasants. each unit would count as 2 of the previous ... so 1 regiment would count for 4 company slots, and 1 platoon would count as 2 company slots. In this set up, you would still have 3 company slots open, in case you wanted to train 3 different companies of something (or 1 platoon and 1 company), or 6 parties or 12 individual units.
It does, however, seem to overly complicate the game without adding a whole lot.