A fair amount of onboard-pres have a gain dial inside the cavity so that you can adjust the level at max-volume. This is so you can account for different output levels coming from different pickups depending on the bass you install the pre on, and adjust so that the output volume is the same as the passive output volume. You could just boost the gain so that the active signal is louder than the passive.
Of course, you'd also have to account for how much gain you can boost coming into the pre before it distorts onboard. If you boost it too much your onboard-pre will clip.
But i'm not really sure what a boost would be useful for. That's kinda what the amp's gain or volume knobs are for. If you need more volume, just raise the volume on the back end where you have a ton of power boosting that signal and pushing it through the speaker.
Boosting the signal on the front end is just gonna cause issues down the line. All your gear between your bass and your amp, including the amp is expecting signal at instrument level. If you start boosting the signal too much, it might be too hot for your gear and you'll need to use gear for Line Level signal or risk ruining your pedals and amp. (I honestly have no idea if onboard pres can boost to line level or not, but it's something to consider if it is possible.)
Also, other issues arise. Like, if the center-detent in active is at unity with the passive full-volume, what happens when you put the bass in passive mode at the center detent? Does that mean the volume is now at 50% because the volume pot is at the center-detent (50%)? Or is the passive volume at 100% when the pot is at the center-detent, and turning the knob past center does nothing? Even if you put a center-detent to make it seem like it's a boost/cut, it's still really just acting like a regular volume knob with an arbitrary detent in the middle. But all the way down is no volume, and all the way up is full volume.
And if your amp's gain is set up to the sweet spot when you're at unity/center-detent, boosting the level on the bass will make the amp start clipping/overloading. But if you set your amp's gain up for full-boost, but then play at unity, your input volume will be too low for the gain stage most of the time until you boost.
If you need more volume, turn up the amp.
If you want to replicate a "boost" control, set your bass full volume, set up your amp to be as loud as you want the boost to be, and then play with your bass's volume at 75% (or whatever)the rest of the time when you're playing for non-boost.