The best replacement for cmmi is itil.

The best alternatives to cmmi are rated as following:
★★★★★  itil
★★★★★  agile
★★★★  iso
★★★  cmm
★★★  six sigma
★★  spice
★  scrum
★  pmi
★  iso 9000
★  lean six sigma
★  pmbok
★  pcmmi
★  tmmi
  iso 15504
  cobit
  iso 9001
  efqm
  opm3
  sw cmm
  automotive spice

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Speaking about cmmi, one probably shouldn't forget about itil.

Other search terms related to cmmi and their ratings are:
★★★★★ itil
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Google Trends

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cmmi
itil
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