Haraka, a multi-nozzle system much as you suggest was under test at White Waltham before the project was cancelled.
For most of the demonstration flights, the tip jets were fitted with 7-lobe silencers, reducing the noise by some 7 db compared to the prototype.
The multi-nozzle system used 9 nozzles per blade with 'double H' silencers fitted to each. Test results showed that a reduction of at least 16 db could have been expected.