1) Similar to retired13's comment, I feel that an important aspect of this is identifying the
reasons for your column moments being as they are. Can you elaborate?
2) What are the dimensions of your column and is it strong or weak axis moments causing the issue?
3) To gauge how much moment we're talking about, what is your load eccentricity? e = M/P?
4) You can tinker with stiffness as long as you're approach to that is realistic and, as JAE mentioned, gives due account to the presence of axial load.
5) You might shed moment from your column by stiffening up the beams / slabs delivering moment to your columns.
6) As Celt83 alluded (I think), your situation might benefit from a column design that accounts for slenderness and P-Little-Delta amplification by way of more advanced procedures such as baking that stuff into your initial model. The classic code provisions for slender columns can be quite conservative. Here are a couple of good articles to get you started along the path to righteous, slender column design:
a)
StructureMag
b)
The Late/Great MacGregor
7) One "cheat" that I know of is to design your column as K=1.0, pretending that it's pin-pin, but then:
a) Use seismic capacity design factors on your material factors and;
b) Keep your axial load level below the balanced point on your interaction diagram.
This usually ensures that your rebar would yield in tension (ductile) before your concrete would crush in compression (less ductile). Unfortunately, this procedure in and of itself usually leads to a pretty stocky column.