You could also go for

JEM
Jemima with any "E" name Elizabeth, Eve, Eliza, Elise etc
Jeremy Edward, Evan, Ewan etc -have know a few Jeremy's shorted to Jem

GEM
Gemma Elizabeth, Eve, Eliza, Elise etc

SIM
Simone Isabelle or Isla or Ida, Ilsa
Simon Isaac, Isaiah, Ignatius (was good enough for Cate Blanchett!)

CIM

Cimon (pr - Sea-Mon) girls name again with any "I" name Isabella, Ilaina,Ilana, Ilona

Would be cool if you could do it again.