It was not possible in this A20 version and isn't in the A21 version. However, both the Coops and Hives are being used in Preppocalypse and Wild West Mod and they allow them to be broken at laying stage and they drop back into the player inventory to be placed again. This is similar to how the Dew Collector used to drop back into the player inventory, but now only drops a Water Filter with a 50% chance.
I shall discuss this with Oakraven for A21. The A20 version is kind of in the archives now and not being touched. This is how it will potentially work for A21 and is how Preppocalypse and Wild West Mod do it.
1. Place a coop or hive. In that empty stage it can be picked up and moved.
2. Add Queen Bee or Chicks.
3. At this stage, once added, the player can break the hive and it drops back to player inventory but the Queen Bee is lost. For the Coop, it has to go one more step to laying stage. As with the hive, the coop can be broken and drops back into the player inventory.
This shouldn't be an issue to add this feature since the player will lose their Bee or Chicks and it can't be exploited in any way. Server Admin can accept that.