ANYTHING GOES begins at the New York sailing of the Ocean Greyhound AMERICA bound for England.  The whole show takes place aboard the ship.  There is a wide variety of characters sailing on the AMERICA.  Reno Sweeney, famed Evangelist-turned-Nightclub singer, with her 4 beautiful Angels (backup singers), Elisha Whitney (Billy's boss and Wall Street executive), Sir Evelyn Oakleigh (a rich English gentleman), Hope Harcourt (Billy's love interest and Evelyn's fiancee), Mrs. Wadsworth Harcourt (Hope's mother), Bishop Henry Dobson (a minister), and Ching and Ling (2 of the Bishop's Chinese converts who like to gamble).

 

Billy comes aboard to drop off his boss' passport and runs into his old friend Reno.  As he starts to exit, he runs into Hope and decides to sail to England after all even though he has no luggage or a room or a passport.

 

Moonface Martin is a gambler and Public Enemy #13.  He is hiding out onboard disguised as a minister.  Billy wins Moonface's friendship by inadvertently identifying the Bishop as Moonface to the FBI.  The Bishop ends up in the ship's brig.  Moonface shows his gratitude by giving Billy a ticket and passport, intended for his friend Snake Eyes, for the trip.  Snake Eyes is number 1 on the "Wanted" list so decides to keep low and not sail.

 

Billy finds out that Hope is engaged to Sir Evelyn and is none too happy.  He enlists the help of Reno to keep Evelyn away from Hope.  In the meantime, he realizes that his boss, Mr. Whitney, is in the cabin across the hall.  Moonface helps Billy out by stealing Mr. Whitney's glasses.  Whitney spends the remainder of the cruise practically blind.

Moon finds out that the authorities are searching the ship for Billy, aka Snake Eyes.  Billy in turn is forced to wear numerous disguises to keep from being caught by the FBI.

 

Reno and Evelyn fall in love but Evelyn, being a true gentleman, feels he must keep his agreement with Hope's mother to marry Hope.

 

Billy is eventually caught by the Purser but the passengers think it's exciting to have Public Enemy No. 1 aboard so he avoids being arrested.  Hope, however, is not impressed and refuses to have anything to do with Billy.  Billy finally confesses he's an imposter, Moonface admits who he really is, and the two end up in the brig.

The 2 Chinese converts end up in the brig with them for gambling.  Billy and Moon trick the  converts into giving them their clothes and are released from the brig disguised as the Chinese.  They crash the wedding ceremony as does Reno who poses as a Chinese girl that Evelyn supposedly had a romp in the rice paddy with and got pregnant.  Mrs. Harcourt is outraged and calls off the wedding.  Reno gets Evelyn, Hope gets Billy, and Moonface finds out he is no longer wanted by the FBI- which is very disappointing to him.