I may do a poor job explaining this, but if you run a BDDI with no blend, you essentially have a flat boost box with bass and treble EQ available. As you turn the blend up you introduce the Sans Amp voicing circuit mixed with your original signal. At 100% blend, you are only getting the Sans Amp voicing circuit which is designed with mid scoop. As the Sans Amp circuitry is introduced the Drive and Presence controls now become active as well.
If you want more mids, you can turn down the bass and treble and increase the Level control (straight gain) to make-up the volume loss. This will reduce the amount of bass and treble frequencies while passing more mids and basically giving you a tone that is more mid focused/present. The other trick is to back off on the blend and allow more of your own bass signal to be present. Assuming you haven't dialed in a mid scoop on your bass or some other pedal, you will get a higher mid content. So you reduce the blend to about 50%, turn down bass and treble controls, use the Level control to recover volume as needed and you get more mids in your sound.
The Drive and Presence controls shape the character of the Sans Amp Circuit effect. While Presence will enhance some higher frequency content, it seems a bit more complex than that and in frequency plots I've seen actually alters the harmonics as well. The Drive control pretty much determines the degree of overdrive you're getting (just like in an amp) and along with the Presence control let's you shape the kind of amp/cab emulation you're getting.
One last point that is essential to keep in mind is that the Sans Amp was designed to be exactly that - no amp! When used to go direct to a mixer it works really well and the lack of mids deal is not at all extreme, it is simply part of the tone and sounds like a mic'ed cab. When folks started using it as a pedal in front of an amp and cab (that frequently produce a mid scooped tone), they got a double mid scoop effect. This is where you need to be creative with your EQ controls and recognize that doubling "a good thing", isn't always a great thing!
I hope that helps...the Tech 21 guys would have probably explained it better.