It could be interesting to be able to run the LRA asynchronously, by having the coordinator executing operations over individual participants. 

mstefank did a PoC called LRA Definition:   

https://github.com/xstefank/lra-executor-extension/blob/master/lra-executor/src/test/java/org/xstefank/lra/execution/LRAExecutorTest.java#L134-L154  

This could be a nice addition to Narayana and later to the specification.