I have the HD-350 head that has a basic SS overdrive in it that is one of the Multidrive settings. It adds a hint of dirt and mid range richness. It also provides a FAT recorded sound. Between that and the EBS compression, I feel I am completely "colored" EBS. I tend to run it at 50% to 75% all the time
I bought the head about 6 years ago when I was rediscovering bass (went from an old Peavey to the EBS). I remember playing around one day a few weeks after the purchase and starting to wonder if I had fallin' for a one trick pony of a bass head. I cranked the Drive knob after a lot of messing around and a big smile came across my face. A whole new world of vintage tones were hiding in there. And I have never turned it back down.
Not the best playing, but here's a direct from the HD-350 balanced out. Compression engaged. Overdrive set at 75%. Bass Flat. Treble Flat. Slight 800Hz boost. Bright at 0. 61J with TI Flats.
EBS HD-350 Drive at 75% 61J TI Flats