Custom boombox question

I have a custom
Box box with 2 4 inch speakers. They sound terrific with them. But lack the bass. I’m wondering if it’s possible to make a separate boom box with a small sub to pick up the bass. Like put in a y-splitter cable to connect them at the RCA plug. If not possible. What speakers would do really well to hit as many sound frequencies as possible??

 

If you build it yourself then you better replace the whole unit with someting new.
Some speakers just cant go low because of theire characteristics.
If you don't want buy a commercial unit, look for chassis dedicated for sub-woofer systems. They are expensive!
Else you end up with a Big box, or a real boom box with a weak base with no attack ...
If you look for a speaker that has the widest bandwith, ( hit as many... ) then a full-range will do, but they are never subwoofer alike and ar far from a smooth response..

Never any speaker can do it all, its fisically impossible. Although some sounds nice.... if you don't listen carefully