  Recent work has shown that the Constrained Minimal Supersymmetric Standard
Model (CMSSM) can possess several distinct solutions for certain values of its
parameters. The extra solutions were not previously found by public
supersymmetric spectrum generators because fixed point iteration (the algorithm
used by the generators) is unstable in the neighbourhood of these solutions.
The existence of the additional solutions calls into question the robustness of
exclusion limits derived from collider experiments and cosmological
observations upon the CMSSM, because limits were only placed on one of the
solutions. Here, we map the CMSSM by exploring its multi-dimensional parameter
space using the shooting method, which is not subject to the stability issues
which can plague fixed point iteration. We are able to find multiple solutions
where in all previous literature only one was found. The multiple solutions are
of two distinct classes. One class, close to the border of bad electroweak
symmetry breaking, is disfavoured by LEP2 searches for neutralinos and
charginos. The other class has sparticles that are heavy enough to evade the
LEP2 bounds. Chargino masses may differ by up to around 10% between the
different solutions, whereas other sparticle masses differ at the sub-percent
level. The prediction for the dark matter relic density can vary by a hundred
percent or more between the different solutions, so analyses employing the dark
matter constraint are incomplete without their inclusion.
