We present an optical/near-IR survey of 11 variable young stars (EXors and EXor candidates) aimed at deriving and monitoring their accretion properties. About 30 optical and near-infrared spectra (
R
∼
1500
–
2000
) were collected between 2014 and 2019 with the Large Binocular Telescope (LBT). From the spectral analysis we have derived the accretion luminosity (L
acc ) and mass accretion rate (
M
̇
acc
), the visual extinction (A
V), the temperature and density of the permitted line formation region (T, n
H), and the signature of the outflowing matter. Two sources (ASASSN-13db and iPTF15afq) have been observed in outburst and quiescence, three during a high level of brightness (XZ Tau, PV Cep, and NY Ori), and the others in quiescence. These latter have L
acc and
M
̇
acc
in line with the values measured in classical T Tauri stars of similar mass. All sources observed more than once present L
acc and
M
̇
acc
variability. The most extreme case is ASASSN-13db, for which
M
̇
acc
decreases by two orders of magnitude from the outburst peak in 2015 to quiescence in 2017. Also, in NY Ori L
acc decreases by a factor 25 in one year. In 80% of the sample we detect the [O i] 6300 Å line, a tracer of mass loss. From the variability of the Hα/[O i] 6300 Å ratio, we conclude that mass accretion variations are larger than mass loss variations. From the analysis of the H i recombination lines, a correlation is suggested between the density of the line formation region, and the level of accretion activity of the source.