There's more than enough gain in the preamp (even without the sat switch) for Thrash, so I'm assuming you want a tighter response from the low end, and perhaps a bit of an aggressive midrange color.
I would start with a relatively inexpensive basic tubescreamer or SD-1, and then if you decide you don't need the extra boost+grit, but the midrange color is what you needed, perhaps an EQ would be in order. Empress Parametric, LWA Brick, MXR 10 band, boss GE7, etc
If you decide coloring the midrange isnt what you needed, but the added grit or boost IS, perhaps a CAE/MXR line driver, BB, Dunlop EP boost, Keeley katana, etc.
If you want to blend the OD with the BEs gain, as mentioned the La Grange would be a good choice - and a million others. Klone work well too. Whatever flavor, you'll need to turn the gain on the amp *down* in combination with the pedal most likely.
If you don't think the BE on it's own has enough gain, there might be something wrong with it, or you might seriously misunderstand how much gain is being used on thrash guitar recordings.