Layering monophonic MIDI Instrument

When playing through a monophonic instrument, duplicating the track and playing the same instrument on top of a recorded layer does not avoid the notes cutting each other off. The only thing I can think of is to render the midi part to audio and then record another layer on top. Is there a way around this so that rendering MIDI to audio is not necessary?

Right click the VST plugin and click copy setting. Open another instance of the VST plugin and paste the setting. Route the duplicated track to this instance of the plugin.