To combine rotations, I believe you canjust multiply that quaternion with a quaternion for each of the other axis rotations you require.
For example, in this simple (extension) method I wrote, I get the final quaternion by combining 3 quaternions for X, Y and Z rotations.
//Takes in angles in degrees
//Useful wiki page: http://www.ogre3d.org/tikiwiki/Euler+Angle+Class and http://www.ogre3d.org/tikiwiki/Euler+Angle+Class+Mogre
public static Quaternion ToOrientation(this Vector3 vec)
{
Quaternion xRot = new Quaternion(Math.DegreesToRadians(vec.x), Vector3.UNIT_X);
Quaternion yRot = new Quaternion(Math.DegreesToRadians(vec.y), Vector3.UNIT_Y);
Quaternion zRot = new Quaternion(Math.DegreesToRadians(vec.z), Vector3.UNIT_Z);
return xRot * yRot * zRot;
}
I must admit my knowledge of quaternions is not amazing, so any expansions on this answer would be appreciated.
Good luck! :)