  In natural duality theory, the piggybacking technique is a valuable tool for
constructing dualities. As originally devised by Davey and Werner, and extended
by Davey and Priestley, it can be applied to finitely generated quasivarieties
of algebras having term-reducts in a quasivariety for which a well-behaved
natural duality is already available. This paper presents a comprehensive study
of the method in a much wider setting: piggyback duality theorems are obtained
for suitable prevarieties of structures. For the first time, and within this
extended framework, piggybacking is used to derive theorems giving criteria for
establishing strong dualities and two-for-one dualities. The general theorems
specialise in particular to the familiar situation in which we piggyback on
Priestley duality for distributive lattices or Hofmann--Mislove--Stralka
duality for semilattices, and many well-known dualities are thereby subsumed. A
selection of new dualities is also presented.
