Parsing inflected forms may not always work as expected. If the following does not give the correct word, try Latin Words or Perseus.
mūtĭto, 1, v. freq. a. [1. muto], to interchange, to appoint by turns; hence, to invite by turns, give mutual invitations (ante-class.): principes civitatis, qui ludis Megalensibus antiquo ritu mutitarent, id est, mutua inter se convivia agitarent, Gell. 2, 24, 2; 18, 2, 11.