With the stringent requirements introduced by the new sixth-generation (6G) internet-of-things (IoT) use cases, traditional approaches to multiple access control have started to show their limitations. A new wave of grant-free (GF) approaches have been therefore proposed as a viable alternative. However, a definitive solution is still to be accomplished. In our work, we propose a new semi-GF coordinated random access (RA) protocol, denoted as partial-information multiple access (PIMA), to reduce packet loss and latency, particularly in the presence of sporadic activations. We consider a machine-type communications (MTC) scenario, wherein devices need to transmit data packets in the uplink to a base station (BS). When using PIMA, the BS can acquire partial information on the instantaneous traffic conditions and, using compute-over-the-air techniques, estimate the number of devices with packets waiting for transmission in their queue. Based on this knowledge, the BS assigns to each device a single slot for transmission. However, since each slot may still be assigned to multiple users, collisions may occur. Both the total number of allocated slots and the user assignments are optimized, based on the estimated number of active users, to reduce collisions and improve the efficiency of the multiple access scheme. To prove the validity of our solution, we compare PIMA to time-division multiple-access (TDMA) and slotted ALOHA (SALOHA) schemes, the ideal solutions for orthogonal multiple access (OMA) in the time domain in the case of low and high traffic conditions, respectively. We show that PIMA is able not only to adapt to different traffic conditions and to provide fewer packet drops regardless of the intensity of packet generations, but also able to merge the advantages of both TDMA and SALOHA schemes, thus providing performance improvements in terms of packet loss probability and latency.