Subject: Can a sphere have more than one axis of rotation?

I've ocassionally pondered this question and have not been
able to intuit a solution.  Take a sphere with a
center point C and spin it a around its X-axis (i.e. the
line XC).  If you then somehow apply a spin around the (original)
line YC, does the sphere have two axes of rotation or does it
now have one axis of rotation which is some summation of
the two spins?

I'm not even sure that my question is well-formed, because
I don't know if you could actually apply a spin to the resting
line YC independent of the spin already given around XC.  For
example, if the sphere has attitude control jets on its sides like
a spaceship, the Y jet would move through the YZ plane (afterstarting the X-spin) and not be able to impart a pure Y spin.

To make this question even more complicated, the earth spins
around it's single axis, but that axis itself precesses. Can
this be thought of as two axes of rotation or are my definitions
just broken?

Thanks for any light you can shed on this puzzle.

Re: Can a sphere have more than one axis of rotation?