  Supersymmetric models with a strongly interacting superconformal hidden
sector (HS) may drive soft SUSY breaking scalar masses, bilinear soft term B\mu
and Higgs combinations m_{H_{u,d}}^2+\mu^2 to small values at some intermediate
scale, leading to unique sparticle mass spectra along with possibly diminished
finetuning in spite of a large superpotential $\mu$ parameter. We set up a
computer code to calculate such spectra, which are then susceptible to a
variety of constraints: 1. possible charge-or-color breaking (CCB) minima in
the scalar potential, 2. unbounded from below (UFB) scalar potential, 3.
improper electroweak symmetry breaking, 4. a charged or sneutrino lightest SUSY
particle (LSP), 5. generating m_h~ 125 GeV, 6. consistency with LHC sparticle
mass limits, and 7. naturalness. We find this bevy of constraints leaves little
or no viable parameter space for the case where hidden sector dynamics
dominates MSSM running, even for the case of non-universal gaugino masses. For
the case with moderate HS running with comparable MSSM running, and with
universal gaugino masses, then the finetuning is ameliorated, but nonetheless
remains high. Viable spectra with moderate HS running and with low finetuning
and large mu can be found for non-universal gaugino masses.
