  I study generalisations of U-duality transformations which do not rely on the
existence of isometries. I start by providing more details of a recently
proposed generalised U-duality map between solutions of type IIA supergravity
of the form $\text{M}_7 \times \text{S}^3$, with NSNS flux, and solutions of
11-dimensional supergravity, in which the three-sphere is replaced by a
four-dimensional geometry which encodes three-algebra structure constants. I
then show that when $\text{M}_7$ admits two abelian isometries, TsT
deformations on the IIA side become six-vector deformations in the
11-dimensional setting. These six-vector deformations involve an action of
$\mathrm{E}_{6(6)}$ on both isometric and non-isometric directions. I discuss
the algebraic interpretation of these deformations, and compare and contrast
them with (generalised) Yang-Baxter deformations in supergravity.
