Well, you'll hear people argue both ways on this based on the personal experience, I think the consensus has always been that Vox's are very fickle when it comes to dirt pedals. I believe a lot of this has to do with their midrange and, especially, their big upper-mid chime. Instead of complementing the Vox voicing, often OD and fuzzes end up compounding it to bad results.

I believe this carries over to Matchless and, by extension, Bad Cat models as well. But with these you have the stiffer feel fo the beefed up filtering.

I don't know of an easy fix to make it make pedal friendly (I have to fully admit, I have little personal experience with Bad Cat and it's clones), but a lot of it is going to be finding the best pedals for the amp.  

There is always the wild card...speakers...these can often make or break distortion tones. It's pretty hard to ever make a Greenback seem harsh, it smooths out everything.

I have a pretty large collection of distortion, overdrive and boost pedals.  Every amp seems to like different stuff, so I've kept a lot of them around.  I am an admitted "pedal guy," and know some amps input impedance are such that they do not play well with pedals in front.  But I just got a hold of a nice SC30 and am having no trouble finding great sound combos for this amp at all.  I love the Fulltone Fat boost into an Electro-harmonix "Analogizer" and then the front of this amp.  It's a combo that just screams.  I can easily hold notes almost as long as I want.  Also the tone knob on my fat boost really smooths out the high end nicely.