The mids you currently have are popping at high volume because you are feeding them too low a frequency. For the same power level a speaker tries to move twice as far at half the freq. For example, your mids would probably be fine if you highpassed them in the 120hz range, but at 60hz they would reach their max excursion and then some with the same amount of power. By adding a dedicated midbass, you can move the crossover point higher and they won't pop at all.
The next problem with your idea is that you will have to feed the new midbass and the current midrange the same frequencies. The frequencies, not the power are causing the popping. You need to send these freqs to the new midbass to get any midbass response and the current midranges clearly can't handle them, so simply adding another driver to the mix wont fix this.
Problem three is cancellation. If you add another midrange and expect that to fix the lack of midbass response without addressing cancellation issues and have them playing the same frequencies, chances are you will do more harm to the response of the system than good and what litle midbass you do currently have will go away. Adding a second tweeter will also trash the high freq response of the system and leave you with a nasty, peaky response. Ading extra tweeters to a system when you care about he quality of the sound is one of the last things you really want to do.
I'm at a loss as to why you think that adding a second of a midrange that isn't producing adequate midbass and can't handle the frequencies in question without bottoming out is going to help the problem anyway.
You need a different driver to get good midbass. The 5 1/4s that you have now will not suffice and adding a second on each side won't help either. You need to provide power to that new driver to get good results from it. By running the new midbass on a seperate amp channel, you can set different frequencies for the midbasses and the midranges in the component set. You can also control the relative level of the midbasses and the components. You said the components were loud enough for you. The ammount of power that gets them loud enough for you will not be enough for good midbass. By wiring them on to the same channel, you will have the same power going to the comps as to the midbasses. By using the 4 channel amp to run the whole of the front stage, you can dial down the comps and still let the midbasses get the powr they need to perform.