Is there any rule that prohibits going back to amend 2019 return to not take home exclusion and then take the exclusion in 2021 for a different home?

My client sold their main home in 2019, which they qualified for used the home exclusion for the gain. Then they sold another home in 2021 that they owned before the one sold in 2019. It meets the home exclusion requirements except for the 2 year look back period. They don’t meet any of the exceptions. The gain in 2019 was about $80k vs $160k in 2021. Are there rules that would prohibit amending 2019, paying the tax on that $80k gain, and then using the exclusion for the $160k this year?