This post isn't intended to be a comprehensive list of every known modification for the Large Beaver, but rather a starting point for those wishing to experiment with the circuit.
OTHER BMP VARIATIONSThere have been many variations of the Big Muff Pi and much discussion about how they compare, but one thing that hasn't changed much is the basic circuit. Sure, you'll find variations in the values of various resistors and capacitors, but nearly all BMP versions (we'll ignore the late '70s opamp version) follow the same basic layout - even the original PNP version.

The two shaded components in the above skeleton schematic - a capacitor in the feedback loop of Q1 and a base resistor on Q2 - don't appear on the Large Beaver circuit board due to the particular variation it clones, but these are easy enough to add if you wish to clone a different BMP model. With a schematic for the desired version and the information contained in the Large Beaver walkthrough, you should have no trouble making a Ram's Head or Russian clone, or even a clone of a non-EH BMP derivative such as the Swollen Pickle.
TRANSISTOR SUBSTITUTIONSIt's been said that the key ingredient to the BMP's sound is the transistors. Others have stated just the opposite - that any high-gain transistor will sound about the same in this circuit. There's something to the latter statement, and you only need to refer to the schematic of the effect to see why. Notice the clipping diodes in the feedback loops of Q2 and Q3. The diodes are the components that actually clip (or distort) the signal. The transistor is simply there to provide clean gain.
As for myself, I take a middle-of-the-road approach. Yes, changing the transistor type can affect the character of the distortion, but there are many other parts in the circuit that can have a more profound affect on the pedal's sound. I've built examples with hand-picked 2N5113s, 2N5088s, and 2N5089s that sound very, very similar, and yet others using the same transistor types - with other resistor and capacitor modifications - that sound dramatically different from one another.
Popular transistor types for this circuit include the BC239, 2N5113, 2N5088, and 2N5089, but many other medium to high-gain NPN silcon transistors will work as well. Socket your transistors and experiment away.

Note that I've seen at least one source of BMP information that indicates the 2N5087 is an acceptable lower-gain alternative to the 2N5088. This is incorrect. The 2N5087 is a PNP analog of the NPN 5088 and will not work in a Large Beaver circuit without other changes (specifically, rewiring the pedal to positive ground).
Use a DMM with a transistor socket to measure the gain (hFE) of each transistor before you begin your build. I like to put transistors with similar gain in the Q2 and Q3 clipping stages. If one of the remaining transistors is significantly lower in gain than the other, put the highest one in Q1 and the lowest in Q4. Why? Because the Q4 transistor in the output stage isn't being asked to do much - it's a simple recovery stage for the loss in gain incurred in the tone stage. In contrast, Q1 in the input stage sets the gain for the entire circuit.
CONVERSION TO PNPPolarity doesn't have a "sound." If you want to convert your pedal to positive ground like the first edition triangle, fine, but don't expect flipping the polarity alone to change the tone of the pedal. If you've got a specific PNP transistor you'd like to try that isn't available in NPN form, then the exercise might be worthwhile. Otherwise, I'd leave the circuit negative ground for a number of reasons and look to other modifications to alter the tone.
BIAS CHANGESIn a stock build, the Q2 transistor in the first clipping stage is mis-biased. This is a result of the circuit conforming precisely to the published schematic for an NPN triangle-era BMP. All other BMP variations I've seen include this resistor. Its omission doesn't create a major problem - there are lots of fine-sounding Beavers out there that don't have it - but we can still make it technically correct. One only needs to top-mount a resistor from the base of Q2 to ground to bring the voltage at Q2's collector up to ~4.5V.
With the circuit board silkscreen-up and the notched edge at the top, the resistor to be added will go in the upper-right corner of the board and will join the topmost leg of the 8.2K resistor nearest Q2 with the topmost leg of the 2.7K resistor at the right-hand edge. An 82K resistor should get Q2 pretty close to 4.5V. Here's a picture of what it looks like...

Virtually every BMP variation has differences in the values of resistors that connect to power or ground - the ones oriented vertically in the schematic. Pick up a schematic for one of these variants and experiment away.
CREAMY DREAMER MODOne popular mod is to jumper the emitters of transistors Q1, Q2, and Q3 directly to ground. This is often referred to as the "Creamy Dreamer" mod. If you're into Gilmour-ish BMP tones, you might want to give this one a miss, as it yields a massive increase in gain and distortion. But if you're after a more Pumpkins-like tone, give it a try. Socketing these resistor pads will allow you to experiment with resistors and jumpers in these spots.
CAPACITOR CHANGESAnother thing unique to the NPN triangle schematic compared to other BMP variations is that it is missing a capacitor in the feedback loop of Q1. This cap acts as a simple low-pass filter which prevents some of the higher frequencies from being passed on to subsequent stages. The addition of this cap won't dramatically change the tone of the pedal, but may help to remove some high-end "gritchiness" from the tone. Values from 470pF to 560pF work well. Adding the cap to the Large Beaver board is a simple process that involves bridging the existing 390K resistor in the input stage.

The 560pF caps in the feedback loops are probably best left stock, but there's nothing magical about the value, so experiment if you want a softer or harder-edged distortion tone.
If you're sourcing your own parts, don't worry about finding precise .05uF caps for the clipping stages. Those are primarily there to block DC and not as tone shapers, and any value between .05uF and .1uF will work just fine.
Leave the remaining .1uF coupling caps at their stock values.
The best place to experiment with other capacitor values is in the tone stack, which we'll cover later.
DIODE CHANGESJust like any other diode clipping circuit, the diodes in a Large Beaver can be changed to provide different sounds. Because there are two clipping stages, you'll probably want to start by modifying just one of the clipping stages (the second) while leaving the other clipping stage stock.
You can use a different kinds of silicon diodes, germanium diodes, LEDs, or even FETs to clip the signal. The diodes from one or both clipping stages can also be lifted, a la the BYOC Mighty Mouse. While I haven't performed this particular mod myself, I imagine that fuzz would decrease and overall volume would increase pretty significantly.
SIMPLE MIDRANGE ADJUSTMENTRaising the value of the 39K resistor to ground (the one next to the .0039 cap) towards 100K will reduce the midrange notch and allow more bass frequencies through when the control is turned towards the treble side. Lowering the value will obviously increase the midrange dip.
Alternately, raising the value of the .0039uF cap to around .0056uF will have approximately the same effect. Going further to 0.01uF will completely flatten the dip. Why? Check out the tone stage on the schematic. The tone two filters now have identical component values - a 39K resistor and a 0.01uF cap - just oppositely oriented.
I recommend using socket pins in these component spots if you want to experiment. That way, you can easily try different resistor or capacitor values to tailor the effect's midrange response to your liking.
TONE STACK CHANGESThere are many other things you can do with the tone stack to tailor it to your needs. I highly recommend using the Duncan Tone Stack Calculator at:
http://www.duncanamps.com/tsc/The TSC is a nifty tool that has the BMP tone stack as a built-in option. Play with the values until the resulting graph looks like something you want to hear. By changing some of the components in this circuit's simple tone stack, you can decrease, increase, or eliminate the midrange notch, or shift it to a lower or higher frequency.
SCOOP/FLAT/BOOST MIDS SWITCH(This modification comes directly from a byoc post in the old mods section.)
The tone knob in the BMP is a high pass filter and a low pass filter in parallel with the B100k acting as a "mix" between the two.
If you use two equal value caps in the two filters, you will get a flat response at noon on the tone knob. This is why the two "on board" caps have been changed to .0033uf so that when the toggle switch is in the "off" or middle position, the two .0068 caps are lifted out.
By adding a .0068 uf cap in parallel to the .0033uf where the .01uf cap used to be(low pass filter), this would give us approx .01uf again, thus giving use the stock "scooped mids" tone knob.
Flipping the toggle to the opposite "on" position would lift that .0068 and put the other .0068 in parallel to the .0033uf cap where the .0039uf cap used to be(high pass filter) which would produce a mid hump at noon on the tone knob.
IMPROVE CLARITY & DEFINITIONThis one's easy - you won't need to make even a single change to your Large Beaver! If you haven't done so already, order yourself a BYOC compressor kit and build a Ross or DynaComp clone. Place it
before the Beaver in your signal chain, and engage the compressor when you want your lead lines to have extra definition.