Disc non-axisymmetric components, such as spirals and central bars, are nowadays known to play an important role in shaping galactic discs. Here we use Tree-SPH N-body simulations to examine the effect of these perturbers on two aspects: the occurrence of multiple patterns in discs and the effects of radial migration on disc thickening. We find that, in addition to a central bar, multiple spiral patterns and lopsided modes develop in all models. Interaction among these asymmetric features results in a large scale stellar migration. However, we show that, despite the strong radial mixing, discs cannot be thickened sufficiently to match observed thick discs. We relate this to the adiabatic cooling as stars migrate radially outwards. We also find that the bulge contribution to a thick-disc component for an Sa-type galaxy at ∼ 2.5 disc scale-lengths is less than 1% and zero in the case of a Milky Way-like, Sb-type. Our findings cast doubt on the plausibility of thick disc formation via stellar radial migration.