Override terragrunt file with json

I know that it's possible to override a terraform file with json. There is a SO answer that describes how to do that: https://stackoverflow.com/a/60234497/1585507.

Assuming you have an example.tffile, you can override some values in this file with a example_override.tf.json. The advantage is that you can programmaticaly generate example_override.tf.json.

I would like to do the same thing with a terragrunt file.

I have a terragrunt.hcl file containing this:

inputs = {
  my_param = true
}

I tried creating a terragrunt_override.tf.json file (also tried with the name terragrunt_override.hcl.json with this inside:

{
    "inputs": {
        "my_param": false
    }
}

But that didn't work (the error was: No argument or block type is named "inputs".).

Is there a way to do that?