I am aware that there is usually 1 or 2 engineers preforming maintenance checks for a particular avionic system on an aircraft at a given moment. For IMA system, is there often more engineers working to get the maintenance checks completed. Are the maintenance check procedures/tests on IMA systems more complex that would require more people.
Not any more people than any other system. But your question raises a few key points for consideration.
First of all, maintainers don't actually go anywhere near the aircraft if it is not a requirement. I don't agree that there are usually 1 or 2 engineers on an aircraft at any given moment. If it aint broke, don't fix it. Over-maintenance is a cause of systems breaking more often due to factors such as human error, more cycles that could reduce life, etc. So unless there is a reason to be there, they won't be pushing buttons just to see if something is still working. In fact, your foreman/chief would probably ask you why you were touching that aircraft. Valid reasons to be working on the aircraft are most often that the maintenance is called for in the servicing schedule (scheduled maintenance), or it has broken (unscheduled maintenance). There are other exceptions to this including modifications and special technical instructions. These will have slightly different names depending on the local authority under which the aircraft operates.
Second point is that if you have been granted authority, have the current licence and the company policy allows for it, you may be able to perform maintenance by yourself. However, airliners usually (at least in Australia) have an AME (aircraft maintenance engineer) do the work and sign the first level of certification, followed by a LAME (Licenced Aircraft Maintenance Engineer) who certifies that the work was completed in accordance with the approved procedure and issues a certificate of release. This allows the aircraft to go flying again. In general aviation, it is more common for the LAME to do the work by themselves. In this case, they are kind of supervising themselves.
Third point: The complexity of the aircraft's system does not determine the number of "levels" of certification. If anything, it is how safety critical the system is to airworthiness that determines how many people must sign for the job. In some cases, an IMI (Independent Maintenance Inspection) or QA (Quality Assurance Inspection) is called for, increasing the levels to 3. Systems such as landing gear are pretty important so they may have 3 levels, but this isn't always the case. The levels are 1-AME, 2-LAME, 3-Independant. I don't think I've heard of Integrated Modular Avionics requiring 3 levels. As a training manager, I'd just make sure my people have adequate training and are confident. If they aren't confident, part of getting your LAME licence is knowing when to put your hand up and say you can't do something. Much safer to do that than guess what you are doing is correct. Hundreds of lives are at stake. You need to have the knowledge and maturity to be a good engineer.
Another interesting point worth bringing up: The Royal Australian Navy had a Sea King helicopter crash leading to loss of lives during Operation Sumatra Assist. This was for the 2004 tsunami. The cause was the lack of a split pin that should have been installed on the main rotor hub assembly. Long story short, the Navy increased the levels of inspection of this job (and others similar to it) from 3 to 4. Data showed that after this change was implemented, more mistakes happened, which is a bit counter-intuitive. You would think that by having 4 people look at something that it would be safer. Wrong. Data showed that people became more complacent because they thought that someone else would have their back if they were having a bad day. The Navy reverted back to 3 levels, and incidents reduced again.
IMA systems (I assume you mean Integrated Modular Avionics) aren't any more complex than aircraft without it. For anyone who is wondering what IMA is, it is basically a concept of merging what used to me a bunch of separate computer systems into a reduced number of boxes. That way the systems can share computing power. On the 787 these are called CPIOMs (Central Processing Input Output Modules). They've managed to reduce the physical footprint and weight of the entire avionics package than pre IMA concepts. There's actually a good argument to say that it is now simpler, because there are less boxes to maintain than before. System testing (BITE) is still done via an interface in the cockpit and is as easy as before.