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We consider the generalization of the Minimal Supersymmetric Standard Model with spontaneous supersymmetry breaking in some hidden sector. After all heavy fields from hidden sector are integrated out, only fields from SM, MSSM and goldstino multiplet remain in the model. We discuss the possibility of di-Higgs production amplification via process gg → s → hh with scalar particle sgoldstino, which is the superpartner of goldstino fermion. In this process sgoldstino is produced by gluon fusion and then decays to a pair of light neutral (SM) Higgs bosons. We observe two possible regimes of sgoldstino decays depending on parameter choice: domination of gluon decay mode and production of pairs of light neutral Higgs bosons, W-bosons and Z-bosons in relation 1:2:1. We give numerical estimates for borders of regions corresponding to these regimes in parameter space. We also obtain an upper limit for 𝑀3/𝐹 and a lower limit for 𝐹‾‾√ from experimental searches for heavy scalar resonances and determination of gluino mass made by the ATLAS and the CMS collaborations.