  We perform an in-depth analysis of the transformation rules under duality for
couplings of theories containing multiple scalars, $p$-form gauge fields,
linearized gravitons or $(p,1)$ mixed symmetry tensors. Following a similar
reasoning to the derivation of the Buscher rules for string background fields
under T-duality, we show that the couplings for all classes of aforementioned
multi-field theories transform according to one of two sets of duality rules.
These sets comprise the ordinary Buscher rules and their higher counterpart;
this is a generic feature of multi-field theories in spacetime dimensions where
the field strength and its dual are of the same degree. Our analysis takes into
account topological theta terms and generalized $B$-fields, whose behavior
under duality is carefully tracked. For a 1-form or a graviton in 4D, this
reduces to the inversion of the complexified coupling or generalized metric
under electric/magnetic duality. Moreover, we write down an action for
linearized gravity in the presence of $\theta$-term from which we obtain
previously suggested on-shell duality and double duality relations. This also
provides an explanation for the origin of theta in the gravitational duality
relations as a specific additional sector of the linearized gravity action.
