  In models with two sources of neutrino masses, we look at the possibility of
generating maximal/large mixing angles in the total mass matrix, where both the
sources have only small mixing angles. We show that in the two generation case,
maximal mixing can naturally arise only when the total neutrino mass matrix has
a quasi-degenerate pattern. The best way to demonstrate this is by decomposing
the quasi-degenerate spectrum in to hierarchial and inverse-hierarchial mass
matrices, both with small mixing. Such a decomposition of the quasi-degenerate
spectra is in fact very general and can be done irrespective of the mixing
present in the mass matrices. With three generations, and two sources, we show
that only one or all the three small mixing angles in the total neutrino mass
matrix can be converted to maximal/large mixing angles. The decomposition of
the degenerate pattern in this case is best realised in to sub-matrices whose
dominant eigenvalues have an alternating pattern. On the other hand, it is
possible to generate two large and one small mixing angle if either one or both
of the sub-matrices contain maximal mixing. We present example textures of
this. With three sources of neutrino masses, the results remain almost the same
as long as all the sub-matrices contribute equally. The Left-Right Symmetric
model where Type I and Type II seesaw mechanisms are related provides a
framework where small mixings can be converted to large mixing angles, for
degenerate neutrinos.
