Manifold means "of many kinds," with the added suggestion that the number involved is not only large but varied and complex: "The superintendent of the apartment building had duties that were manifold." Multiform means "having many forms of many different kinds": "The obstacles to saving money are multiform, but a strict budget will help overcome them." Multiple means "consisting of many parts or elements": "There are multiple risks in starting a new business." Related words include numerous, multifarious, myriad, sundry, various, and multitudinous.
Dictionary of problem words and expressions. Harry Shaw. 1975.