We could double humanity's genetic "shuffle rate" by allowing couples to have one child naturally but requiring men to donate their sperm to a central bank, and women to carry and give birth to "randomly-fathered" children.
Obviously the institutional and logistical (not to mention ethical) challenges make this impossible in any present society. But for a planned community of fixed size (e.g. a small colony of humans attempting to rapidly populate a planet, or a starship designed to support the minimum possible human population with the highest possible genetic diversity), such measures may be a practical necessity.
I suspect this has been explored in Science Fiction, though I've never read anything in which this idea was put into practice.
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