The ALMA correlator processes the digitized signals from 64 individual antennas to produce a grand total of 2016 correlated base-lines, with runtime selectable lags resolution and integration time. The on-line software system can process a maximum of 125M visibilities per second, producing an archiving data rate close to one sixteenth of the former (7.8M visibilities per second with a network transfer limit of 60 MB/sec). Mechanisms in the correlator hardware design make it possible to split the total number of antennas in the array into smaller subsets, or sub-arrays, such that they can share correlator resources while executing independent observations. The software part of the sub-system is responsible for configuring and scheduling correlator resources in such a way that observations among independent subarrays occur simultaneously while internally sharing correlator resources under a cooperative arrangement. Configuration of correlator modes through its CAN-bus interface and periodic geometric delay updates are the most relevant activities to schedule concurrently while observations happen at the same time among a number of sub-arrays. For that to work correctly, the software interface to sub-arrays schedules shared correlator resources sequentially before observations actually start on each sub-array. Start times for specific observations are optimized and reported back to the higher level observing software. After that initial sequential phase has taken place then simultaneous executions and recording of correlated data across different sub-arrays move forward concurrently, sharing the local network to broadcast results to other software sub-systems. The present paper presents an overview of the different hardware and software actors within the correlator sub-system that implement some degree of concurrency and synchronization needed for seamless and simultaneous operation of multiple sub-arrays, limitations stemming from the resource-sharing nature of the correlator, limitations intrinsic to the digital technology available in the correlator hardware, and milestones so far reached by this new ALMA feature.