  We explore the phenomenology of the full General Gauge Mediation parameter
space in the MSSM focusing on the consequences of having a fundamental Higgs
around 125 GeV. Assuming GUT-complete structure of the hidden sector, we allow
for deviations from the strict definition of gauge mediated SUSY-breaking
coming from mild violations of messenger-parity and from extra couplings
between the Higgs multiplets and the hidden sector. Relaxing the GUT
assumption, our parameter space is defined by the property of having vanishing
A-terms at the messenger scale. In this extended setup we focus on the
possibility of splitting the SU(3) mass parameters of GGM. In all these
scenarios we investigate the possible spectra, discussing to what extent having
an Higgs mass around 125 GeV is constraining the GGM parameter space and what
are the possible signatures at LHC.
