Here's an example of my tasks.json:
{
  "version": "0.1.0",
  "tasks": [
    {
      "taskName": "test",
      "suppressTaskName": true,
      "command": "python",
      "args": [
        "tests/brewer_tests.py"
      ],
      "isTestCommand": true
    }
  ]
}
I can run this with shift+cmd+alt+b. I can also run it with alt+t, and choose it from the menu. Is it possible to pass additional arguments in that menu? e.g.

And you could build it into your task like so:
{
  "version": "0.1.0",
  "tasks": [
    {
      "taskName": "test",
      "suppressTaskName": true,
      "command": "python",
      "args": [
        "tests/brewer_tests.py",
        $arg1                        # would resolve to "ARG1"
      ],
      "isTestCommand": true
    }
  ]
}
Or something similar?