Find a literary agent to represent you. Your agent will pitch your manuscript or manuscripts to book publishers, including Doubleday. The literary agent is better equipped to match the manuscript to a publisher.
Increase your chances of being published by Doubleday by creating a manuscript on a topic which they currently need. For example, nonfiction writers will increase their chances of being published by Doubleday if they write a biography.
Expand your fiction horizons by providing Doubleday with the genres which are not over-represented in their book catalog. Fiction writers who write exciting works of adventure, confession or mainstream fiction will have a solid chance at getting published by Doubleday.
Experiment with different fiction genres in order to get published by Doubleday. Try experimental writing, ethnic fiction, historic fiction, or religious fiction. Find an agent which works with those genres.
Accept offers to be published by a major publishing house, even if it is not Doubleday. It is more important to find a publisher who will pay you an advance and royalties for your work than to try to get published by one specific publisher.