We consider deformations of a differential system with PoincarĂ© rank 1 at infinity and Fuchsian singularity at zero along a stratum of a coalescence locus. We give necessary and sufficient conditions for the deformation to be strongly isomonodromic, both as an explicit Pfaffian system (integrable deformation) and as a non linear system of PDEs on the residue matrix A at the Fuchsian singularity. This construction is complementary to that of (Cotti et al 2019 Duke Math. J. 168 967â€"1108). For the specific system here considered, the results generalize those of (Jimbo et al 1981 Physica D 2 306), by giving up the generic conditions, and those of (Bertola and Mo 2005 Int. Math. Res. Pap. 2005 565â€"635), by giving up the Lidskii generic assumption. The importance of the case here considered originates form its applications in the study of strata of Dubrovin-Frobenius manifolds and F -manifolds. [ABSTRACT FROM AUTHOR]