The best replacement for monogamy is polygamy.

The best alternatives to monogamy are rated as following:
★★★★★  polygamy
★★★  polyamory
★★  promiscuity
★★  open relationship
★★  non monogamy
★  serial monogamy
★  open relationships
  swinging
  genetic monogamy
  monogamy
  modified polygamy
  non-monogamy

Your alternative for monogamy is not listed? Suggest!
Speaking about monogamy, one probably shouldn't forget about fidelity.

Other search terms related to monogamy and their ratings are:
★★★★★ fidelity
★★★★★ commitment
You have in mind a companion for monogamy and it is not yet here? Propose!



Google Trends

Scale is based on the average worldwide traffic of monogamy in all years. Click on graph for more.
monogamy
polygamy
polyamory