Sync between multiple indices

Hi,
I got a requirement of indexing a document in multiple indices each having their own ingestion pipeline.

Constraint: the API call to add a document will only be done to primary index.
Need to build a sync such that document flows through primary index to secondary ones processed via their ingestion pipeline.

Like reroute processor redirects to another index, I want it to be added in both source and rerouted index.

I do believe that is not possible so you would likely need to index directly into multiple indices.