I understand I can't do this straightforward from studying similar questions on stackoverflow and other sites.
However, I need to do this and I'm willing to go with workarounds.
I tried to create a non-unique index with online and parallel, and then drop the old unique index. However, it fails saying ORA-01408: such column list already indexed.
How to convert an unique index to a non-unique one?
Oracle now supports multiple indexes applied to the same set of columns as long as they differ in uniqueness (and/or in some other properties such as bitmap vs. btree and partitioning) and as long as only one of them is visible.
Therefore you can alter the existing index - changing it to invisible without dropping it and then create a new non-unique index.
CREATE TABLE mytable (id NUMBER);
CREATE UNIQUE INDEX mytable_unique_idx ON mytable(id);
ALTER INDEX mytable_unique_idx INVISIBLE;
CREATE INDEX mytable_nonunique_idx ON mytable(id);
Note that invisible indexes are still maintained by the database and you can change between them by turning one of them to invisible and the second one to visible.