I've found that the Hornet and the Portaphile Maxxed (all options) match very well with the K701.
The Hornet has plenty of power and adds its warmth, smooth flow but with solid leading edges, bass punch and energetic/forward presentation for a very musical experience with the 701s.
The Portaphile (with LT1210 & 2x1500uf BlackGate NX caps) brings out the best of the 701's great spatiality & imaging capabilities, extension, inner detail, and also has plenty of power (but no charging circuit and a battery burner), besides adding excellent bass energy and definition. (No external gain switch, but internal accessible dip switches for Hi/Lo gain, class A on/off, hi-bandwidth on/off & LED on/off)
They both offer excellent power and sound quality in small packages, the Hornet offering a slightly smaller footprint, charger, external 3-way gain switch, and beautifully crafted case & fittings.
The AE-2 is also an excellent, smaller amp -- though larger than the Hornet and Portaphile. It can also drive the 701s very well, is quite dynamic and extended, and images very well with the 701s. In some way similar to the Portaphile in this regard, it has a great sense of air around instruments, and offers lots of macro- and micro- (inner) detail, and good layering of instruments.
Do some searching and you'll find plenty of posts about all these amps and more, though 701-specific impressions are somewhat sparse.