Simple Sub Amp Integration

I have a dual mono-block chip-amp (Brian-GT)system that includes a Lightspeed attenuator. Although I am extremely pleased with the low-end output I'm getting with my current M-T-M speakers, once in a while I would like to go for things like those growlers at the bottom of a pipe organ. I have a Hi-Vi SP-10 with *Znom: 4 ohms *Re: 3.4 ohms specks. Can someone suggest a good DIY amp along with the proper integration method - hopefully with the option to completely switch the sub out when not needed?
you will have to make a decision on how you integrate the crossovers (filters) between satellite and bass.

You could use the natural roll off of the satellite and adjust the bass crossover to match this.
Doing this sends the same power and frequencies to your satellite and the bass will suffer the same problems you have at present without the auxiliary bass speaker.

An Alternative is to filter (crossover) the satellite at a higher frequency than it's natural roll off frequency, using the complementary filter to feed the bass speaker.
This reduces the bass frequencies sent to the satellite and allows it to perform a bit better than at present, with the bass speaker taking on the heavy demands for which it is specifically designed.

I see a problem with option one, but I also see a problem with option two. If you run bass and satellite then you get your required integration, turn off the bass and your satellite is filtered to attenuate some of the bass. This will sound odd. You would need to be able to switch out the bass speaker and switch out the satellite filter to properly hear the satellites alone.

When you have made that operational decision then look at the respective voltage and current demands of the satellite and bass to allow selection of suitable amplifiers. The amps decision comes last
Thanks Andy, but I am hoping to do a different approach. I would like to be able to maintain the basic full system on the left and just add what I guess would be a second leg ( on the right) when I want those bottom organ room shakers. I'm not talking about adding the sub per song/track. More correctly - switching it in before I start playing a CD.

I know it's some kind of "Y" connection or preamp configuration but I'm trying to maintain the non-mechanical nature of the Lightspeed if that is possible.I am open to all suggestions.