  We investigate the localization properties of a spin chain with an
antiferromagnetic nearest-neighbour coupling, subject to an external
quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates
between two paradigmatic models, namely the Aubry-Andr\'e and the Fibonacci
models. We find that stronger many-body interactions extend the ergodic phase
in the former, whereas they shrink it in the latter. Furthermore, the many-body
localization transition points at the two limits of the interpolation appear to
be continuously connected along the deformation. As a result, the position of
the many-body localization transition depends on the interaction strength for
an intermediate degree of deformation of the quasiperiodic modulation.
Moreover, in the region of parameter space where the single-particle spectrum
contains both localized and extended states, many-body interactions induce an
anomalous effect: weak interactions localize the system, whereas stronger
interactions enhance ergodicity. We map the model's localization phase diagram
using the decay of the quenched spin imbalance in relatively long chains. This
is accomplished employing a time-dependent variational approach applied to a
matrix product state decomposition of the many-body state. Our model serves as
a rich playground for testing many-body localization under tunable potentials.
