VLAN switch (device) addressing

I was asked a question the other day and it embarasses me to admit that I do not know the answer.

“Does each switch participating in a secondary VLAN require a unique IP address within that VLAN subnet or is one IP address used for all the switch configurations?”

This is in reference to only the switches not the switch ports. I noted that a unique id is required for each switch in the Default VLAN simply to manage the switch but I’m not certain the same is true for additional VLAN’s.

Can any-one set me straight?