I presume that you will want to change all the referencing foreign keys to use the new primary key, right? So you are going to have to drop all these foreign keys, then drop the primary key, then create the new primary key, then create new foreign keys that reference the new primary key. So if there are 10 FKs that reference this table, you'll have to do 10 drops of the FKs, 1 drop of the old PK, 1 alter to add the new PK, then 10 alters to add the new FKs.
I don't have an instance of Postgres handy, but I don't think there's any shortcut to this. I think you have to do all 22 steps. But you don't have to drop the database, just all the FKs.
If you want the old FKs to continue to point to the old PK, which will no longer be the PK when you're done, then as Erwin says, you should be able to just add a unique constraint on it. Though I think his example is backward in that you'd have to add the unique constraint BEFORE dropping the PK or you'd get the same message. As I say, don't have a copy of Postgres handy to check this. In Sql Server, you can add a unique index, then drop the pk, then create the new pk. I suppose worst case would be that you'd have to drop the 10 FKs and then re-create them.