The best replacement for sole custody is joint custody.

The best alternatives to sole custody are rated as following:
★★★★★  joint custody
★★★  full custody
★★  shared parenting
★★  primary custody
★  shared custody
★  joint
★  physical custody
★  legal custody
  custodial parent
  sole legal custody
  joint legal custody
  parental rights

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Speaking about sole custody, one probably shouldn't forget about visitation.

Other search terms related to sole custody and their ratings are:
★★★★★ visitation
★★ visitation rights
You have in mind a companion for sole custody and it is not yet here? Propose!



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