One of the things you need to consider is what I like to refer
proximity-to-clip. Much of what is below will address that notion.
Diode-based clipping circuits work by limiting the headroom
in the device. They set a sort of ceiling beyond which the signal
can't exceed. If any part of the signal exceeds that
ceiling/threshold/limit, it gets clipped and "squared off". As the
signal decays, less and less of it exceeds that threshold, and the
sound becomes less fuzzy.
Now, I know there are many other parameters, but one of the
that most distortion devices share, or rather differ on, is the
relationship between gain structure and clipping circuit. One can
construct different diode-based clipping circuits that raise or lower
the clipping threshold (germanium diodes have a lower threshold and
sound "fuzzier" than Si for that reason, but they also result in less
output if you don't boost the signal afterwards). Those with a
higher threshold will be able to put out much more signal to the amp
(which gets you another source of distortion). However, having a
higher clipping threshold puts your average guitar signal farther
away from the clipping point. You CAN overcome this if you crank up
the gain just ahead of the clipping circuit, in effect moving more of
the overall signal closer to the threshold of clipping (here's where
the proximity-to-clip notion comes in).
So, what could improve proximity-to-clip to get a fuzzier sound?
Virtually any booster stage ahead of the actual pedal: EQ, line
booster, compressor, another overdrive/fuzz. Alternatively, if the
pedal permits, simply increase the gain in any available gain stages
preceding the clipping circuit. The Big Muff Pi, and all its
imitators, is actually two cascaded diode-based distortion stages.
The signal is clipped in the first one, then boosted and clipped
again in the next stage. The second booster stage is needed because,
unless one is using different diodes with a lower clipping clipping
threshold, once clipped by the first stage, the signal will not
exceed the clipping threshold of the next set of diodes unless
boosted again. It is this reboosting and clipping that gets the BMP
its super compressed and drawn out buzz. You can get this with just
about any distortion device, though, as long as whatever is ahead of
it keeps the signal very close to, or above, the clipping point all
the time. If you wanted an excruciating buzz, just build a BMP and
insert a third clipping stage like the second. That oughta do it.