A search for the lepton-flavour violating decays B0 → K*0μ±e∓ and $$ {B}_s^0 $$ B s 0 → ϕμ±e∓ is presented, using proton-proton collision data collected by the LHCb detector at the LHC, corresponding to an integrated luminosity of 9 fb−1. No significant signals are observed and upper limits of$$ {\displaystyle \begin{array}{c}\mathcal{B}\left({B}^0\to {K}^{\ast 0}{\mu}^{+}{e}^{-}\right) B B 0 → K ∗ 0 μ + e − < 5.7 × 10 − 9 6.9 × 10 − 9 , B B 0 → K ∗ 0 μ − e + < 6.8 × 10 − 9 7.9 × 10 − 9 , B B 0 → K ∗ 0 μ ± e ∓ < 10.1 × 10 − 9 11.7 × 10 − 9 , B B s 0 → ϕ μ ± e ∓ < 16.0 × 10 − 9 19.8 × 10 − 9 are set at 90% (95%) confidence level. These results constitute the world’s most stringent limits to date, with the limit on the decay $$ {B}_s^0 $$ B s 0 → ϕμ±e∓ the first being set. In addition, limits are reported for scalar and left-handed lepton-flavour violating New Physics scenarios.