I suppose you mean circles in the literal sense, round circles. I suppose "just three" means "at most three". The answer is "yes".

Let us identify your sphere with the extended complex plane via stereographic projection, so that your circles are straight lines or circles. Consider the following sets $A,B,C,D$.

Let $D=\{ \infty \}$, $C=\{ 0 \}$, $A$ the set of points with argument commensurable with $\pi$, and $B$ the set of points with argument non-commensurable with $\pi$. These sets partition the extended plane. If a circle does not contain $D$, it intersects at most 3 sets. If it contains $D$, it is a straight line. If this straight line does not contain $C$, it intersects at most 3 sets. If it contains $C$, it intersects either $C,A,D$ or $C,B,D$ but not all 4.

Sorry, do not know how to make curly braces {} with Mathjack.