I concur with @Skulliah perfectly correct, you can buy as many as you like, but you have to discard one or complete it, only one can be held at a time. (although I think you could probably put one down on the table, vote on it, and go grab another).

@portal-2-yazdi @Sshteeve

Yes you can only have one in your inventory but you'll be able to purchase another one after :)

@portal-2-yazdi I am unsure as of yet as I have not been able to sail in a couple of days.
Perhaps another @boatswain who may have sailed yesterday can step in to fill the blanks?

@sshteeve Are you only able to have one in your voyage inventory? Sorry, not sure whether I should waste the only one I got when I might have to leave.

@portal-2-yazdi as per the patch notes and the release page, you can buy as many as you want from Duke, so long as you have the 5 Doubloons each costs!