Understood.
A judge may be persuaded that the requirements of justice and or fairness and or even the practicalities of litigation management would dictate the imposition of a stay. Ultimately those decisions require a judge to strike a balance between the competing rights of the litigants and the issues involved. Sometimes a stay can be to the advantage of some parties but very inconvenient to the others, in which case any ruling granting a stay could be appealed but that can then make litigation very messy and even more complex to resolve.
In a way you have probably answered the question where you mention the outcome of one trial affecting another party. If the first trial impacts on the second third party in a particular fashion that may well dictate how they will then proceed with or defend the remaining litigation.
Although there are several distinct pieces of litigation involved it can happen that different actions are all set down for trial and tried together by the same judge. This might happen where there are common issues or common evidence as between the cases but this might not be the case here. Sometimes this is convenient but not always !
Keep in close contact with your solicitor about the levels of costs being incurred as they can rise very quickly as litigation matures....