I can see where the lower mids / upper bass could be missing if your main speakers only have 4-inch woofers. However, it would be best to simply try raising the crossover frequency of the sub.
The reason is, what you’re proposing is going to be a hit-or-miss proposition. Without a crossover between the mains and proposed woofers, the part of the frequency range that they overlap will sound exaggerated. On top of that, if the new woofers are naturally louder, or quieter, than the main speakers (the former is the most likely), there will be no way to adjust their level for a better blend.
Regards,
Wayne A. Pflughaupt