Subsequent completion after insert Follow

Is it possible to retrigger the basic completion behavior after a previous completion has inserted the suggestion.

What I mean is:

<caret> on blank line, user manually triggers completion. One of the provided suggestions is: MyCommand()

MyCommand(<caret>); retrigger completion so the possible values for the first parameter of MyCommand are shown.

So far, I can manage getting the MyCommand inserted and moving the caret between the parenthesis using the InsertHandler. But I can't find a way to then (programmatically) trigger the completion again.

I have a specific CompletionContributor that recognizes when the caret is present in the MyCommand parenthesis but I don't know how to trigger it. This means that the user will have to manually trigger basic completion again while I would like to immediatly show a list with possible values.