Dual Tube SIAB
A Sovtek 12AX7 costs about $10US, so why not build a real guitar preamp?
I can't think of a smartypants name for this (Rocks-in-a-box?) so:
       Dual Tube SIAB Schematic    
There a volume pot for the new stage. This allows you to "pad down" the gain between each amplification stage to get a clean sound, or to allow mild clipping on each stage to get a really smooth distortion sound. Or vicious clipping on one stage to get a vicious sound. So you can have a clean setting or a raging overkill.
The 330k resistor attached to the drive control is the old 680k on the FX in/out, you should change both of them if you want to keep the FX in/out.
No gain without pain: Each tube provides a gain of about x40, so the later stages need thier input divided by 10 or more to prevent fuzz. With all the gain knobs at maximum, you may start to overdrive the speaker sim a little. Maybe some metal film resistors on the plate resistors. If the signal goes anywhere near 40V, it will clip in a fuzzy manner. I upped the voltage from  less than 40V on mine to 57V for more headroom. It hasn't exploded yet.
Using a 12AU7 instead of a 12ax7 in the second position might be better, since it has a lot less gain.

Construction:
Start with a standard PAIA Stack-in-a-box.
I just used perfboard and soldered to the tube pins. You should use a tube socket for the extra tube. The power supply seems to handle the extra tube well enough on mine. The PAIA  Tubehead runs 2 tubes from the same power supply. Disclaimer: Yours may well explode for all I know.
Measure the voltages on your SIAB to check they are correct to begin with. Make sure the extra power connections aren't touching anything they shouldn't.  Keep the tube away from the power supply end, keep wires fairly short.
Heaters: Pin 4 of the first tube goes to pin 4 on the new tube. Pin 5 of the first tube goes to pin 5 on the new tube.Twist the heater cables to reduce noise.
I used a Sovtek 12AX7WA. The Groove Tubes GT-ECC83 has less gain and more midrange. The cheaper Sovtek is fine.

Operation:
Turn the Drive and the new dual pot down to about 20% volume, and turn up the crunch to get some distortion. Ease up the Drive to get a little more distortion, then ease up the new dual pot to get a little more distortion again. Feel free to crank the knobs up more. It will probably make terrible screeching noises at maximum gain. Adjust the physical positioning of the new tube and wiring to minimize this.  All knobs halfway should be enough distortion for decent folk.
Mods:
You can look at guitar amp preamp schematics for ideas. I can put a graphic equalizer or a passive Fender tone stack in the FX in/out. You could add a Marshall-style tone stack between the last two stages if you want.
Increasing B+: There is an array of 5 diodes and capacitors to generate the 40V going to the plate resistor. The pattern is fairly obvious, and you can increase the plate resistor B+ byabout 6V by adding another diode/capacitor. Change C2 to a 100V type if you want to go over 50V with two diode/capacitor stages. Not that this is going to make a big difference to the sound.