how to make block step only unblockable for certain users in my team.
Users need build access to a pipeline in order to build or unblock steps within it.
You could use this env var BUILDKITE_UNBLOCKER in steps that are uploaded and run after the block step to check who the unblocker was and take any necessary action at that point to not allow the step to run, etc
Can you make block step block again after its has been unblock?
No you can’t reblock a block step. There wouldn’t be much point as steps dependent on the block would have progressed and be running.
But you can upload another block step if necessary to fulfill your logic