Rapid progress in optical atomic clock performance has advanced the frontiers of timekeeping, metrology and quantum science. Despite considerable efforts, the instabilities of most optical clocks remain limited by the local oscillator rather than the atoms themselves. Here we implement a ‘multiplexed’ one-dimensional optical lattice clock, in which spatially resolved strontium atom ensembles are trapped in the same optical lattice, interrogated simultaneously by a shared clock laser and read-out in parallel. In synchronous Ramsey interrogations of ensemble pairs we observe atom–atom coherence times of 26 s, a 270-fold improvement over the measured atom–laser coherence time, demonstrate a relative instability of 9.7(4)×10^(−18)/√τ (where τ is the averaging time) and reach a relative statistical uncertainty of 8.9 × 10^(−20) after 3.3 h of averaging. These results demonstrate that applications involving optical clock comparisons need not be limited by the instability of the local oscillator. We further realize a miniaturized clock network consisting of 6 atomic ensembles and 15 simultaneous pairwise comparisons with relative instabilities below 3×10^(−17)/√τ, and prepare spatially resolved, heterogeneous ensemble pairs of all four stable strontium isotopes. These results pave the way for multiplexed precision isotope shift measurements, spatially resolved characterization of limiting clock systematics, the development of clock-based gravitational wave and dark matter detectors and new tests of relativity in the lab.