Is there anyway of adding a custom query string parameter after clicking the Save & Close button?

Thank you for your response. I'm able to set and get the query string param when creating a custom button because adding the query string is as easy as adding it to the URL in the formula field.
The part I'm having trouble with is inside of my script (which is using the IOL technique), I'm unable to set a query string param that will show up in the URL once the page goes from Edit mode back to View (after clicking the Save & Close button).