Can you have a mutual inductance between two inductors which is larger than one of the inductors?
For example: L1= 0.1 nH, L2= 2.5 nH, M=-0.246 nH --> k=-36.2%.
Are these values practical and could the configuration be realized in LTCC or MMIC technologies?
Yep, that's certainly physically possible. The max limit on mutual inductance can be proven through energy conservation, but as long as the coupling coefficient is less than 1 (k = M/sqrt(L1 * L2) ) than the mutual inductance is realizable.
Sorry, but I can't offer any advice as to if those values could be implemented in the way you described.
Doing so requires a large turns ratio between windings. I don't see why it wouldn't be doable so long as you have several metal layers to work with. Can't say what sort of Q to expect though.