  When fitting cross sections with several resonances or interfering background
and resonances, one usually obtains multiple solutions of parameters with equal
fitting quality. In the present work, we find the source of multiple solutions
for a combination of several resonances or interfering background and
resonances by analyzing the mathematical structure of the Breit-Wigner
function. We find that there are $2^n$ fitting solutions with equal quality for
$n+1$ resonances, and the multiplicity of the interfering background and
resonances depends on zeros of the amplitudes in the complex plane. We provide
a simple, general method to infer all other solutions with equal fitting
quality from a known solution.
