I find the practice and poses in doga to be more organic than in a people yoga class...and more so with our larger canine companions. The small dog poses in doga are kind of a no brainer, with the lifting and the balancing. Because of this it can feel more challenging to incorporate the larger dogis into the practice. But really it's just a matter of looking at what you want the pose to accomplish and then modify accordingly.
For example, in Super Dog Stretch you can certainly lift your large dogi if you and your dog are in good physical condition. But if your dog is too heavy or if she's relaxed lying on the mat and it just doesn't seem right to make her stand, you can figure it out. Remember the goal. Super Dog Stretch is stretching the legs from the armpit and also, depending on where the human is in the pose it can be a spinal twist or side waist stretch (see previous post from last week on Super Dog Stretch for deets). So for your big dogi , an option could be to reach under the arm (leg?) pits and massage or stretch outward. No lifting required, there are a couple of other modifications you could do as well but I won't be too long winded. Big Dogi owners...Let me know how it goes.