The Laser Interferometer Space Antenna (LISA) gravitational-wave (GW) observatory will be limited in its ability to detect mergers of binary black holes (BBHs) in the stellar-mass range. A future ground-based detector network, meanwhile, will achieve by the LISA launch date a sensitivity that ensures complete detection of all mergers within a volume >O(10) Gpc^{3}. We propose a method to use the information from the ground to revisit the LISA data in search for subthreshold events. By discarding spurious triggers that do not overlap with the ground-based catalogue, we show that the signal-to-noise threshold ρ_{LISA} employed in LISA can be significantly lowered, greatly boosting the detection rate. The efficiency of this method depends predominantly on the rate of false-alarm increase when the threshold is lowered and on the uncertainty in the parameter estimation for the LISA events. As an example, we demonstrate that while all current LIGO BBH-merger detections would have evaded detection by LISA when employing a standard ρ_{LISA}=8 threshold, this method will allow us to easily (possibly) detect an event similar to GW150914 (GW170814) in LISA. Overall, we estimate that the total rate of stellar-mass BBH mergers detected by LISA can be boosted by a factor ∼4 (≳8) under conservative (optimistic) assumptions. This will enable new tests using multiband GW observations, significantly aided by the greatly increased lever arm in frequency.