Allow no value

I'm trying to implement a string option that can have three states:
1. Not supplied
2. No value
3. Empty or value

I want to do the following:
`MyApp.exe` writes unformatted output to standard output
`MyApp.exe --json` writes JSON formatted output to standard output
`MyApp.exe --json file.json` writes JSON formatted output to `file.json`

Is this currently possible?