  We build on the results of arXiv:1912.11036 for generalised frame fields on
generalised quotient spaces and study integrable deformations for
$\mathbb{CP}^n$. In particular we show how, when the target space of the
Principal Chiral Model is a complex projective space, a two-parameter
deformation can be introduced in principle. The second parameter can however be
removed via a diffeomorphism, which we construct explicitly, in accordance with
the results stemming from a thorough integrability analysis we carry out. We
also elucidate how the deformed target space can be seen as an instance of
generalised Kaehler, or equivalently bi-Hermitian, geometry. In this respect,
we find the generic form of the pure spinors for $\mathbb{CP}^n$ and the
explicit expression for the generalised Kaehler potential for $n=1,2$.
