Dear daescuc, typically, the main memory is critical (size and access speed) to be able to run 2 or more analyses at once without a noticeable slowdown. First of all, make sure there is enough physical RAM memory for both/all analyses (if swapping starts, it can easily slow down the program 100x or 1000x). Second, the memory tranfer rate can be limiting (especially if there are empty memory slots or a mix of modules of differing speeds such that dual or triple channel memory controller can not work efficiently).
With ATENA 3D and large models, storing results to disk can also become a bottleneck easily. Consider only storing every 5th or 10th step to reduce the file size and therefore also the file writing time.
With respect to possible interferences of multiple ATENA instances, there shouldn't be any as long as you do not open the same model file multiple times.