  Given compact Lie groups H\subset G, we study the space of G-invariant
metrics on G/H with nonnegative sectional curvature. For an intermediate
subgroup K between H and G, we derive conditions under which enlarging the Lie
algebra of K maintains nonnegative curvature on G/H. Such an enlarging is
possible if (K,H) is a symmetric pair, which yields many new examples of
nonnegatively curved homogeneous metrics. We provide other examples of spaces
G/H with unexpectedly large families of nonnegatively curved homogeneous
metrics.
