  We analyze the merger and assembly histories of Milky Way (MW) and Andromeda
(M31)-like galaxies to quantify how, and how often, disk galaxies of this mass
can survive recent major mergers (stellar mass ratio $\ge$ 1:4). For this, we
use the cosmological magneto-hydrodynamical simulation TNG50 and identify 198
analog galaxies, selected based on their $z=0$ stellar mass ($10^{10.5-11.2}
{\rm M_{\odot}}$), disky stellar morphology and local environment. Firstly,
major mergers are common: 85 per cent (168) of MW/M31-like galaxies in TNG50
have undergone at least one major merger across their lifetime. In fact, 31
galaxies (16 per cent) have undergone a recent major merger, i.e. in the last 5
Gyr. The gas available during the merger suffices to either induce starbursts
at pericentric passages or to sustain prolonged star formation after
coalescence: in roughly half of the cases, the pre-existing stellar disk is
destroyed because of the merger but reforms thanks to star formation. Moreover,
higher merger mass ratios are more likely to destroy the stellar disks. In
comparison to those with more ancient massive mergers, MW/M31-like galaxies
with recent major mergers have, on average, somewhat thicker stellar disks,
more massive and somewhat shallower stellar haloes, larger stellar ex-situ mass
fractions, but similarly massive kinematically-defined bulges. All this is
qualitatively consistent with the different observed properties of the Galaxy
and Andromeda and with the constraints on their most recent major mergers, 8-11
and ~2 Gyr ago, respectively. According to contemporary cosmological
simulations, a recent quiet merger history is not a pre-requisite for obtaining
a relatively-thin stellar disk at $z=0$.
