Working to build out a model where multiple PMs would setup/manage their project schedules, but share resources across projects.
ProjeQtOr is really good at that
At times there may be a need to show temporary resource conflicts
ProjeQtOr do not manage "conflicts" but may delay some tasks...
From my current testing I've noted that ProjeQtOr attempts to level load resourcing as part of planning
Right

ProjeQtOr will never plan a resource 48 h per day (as MS-Project can do)
While that is the desired end result, there is a need for PMs to be able to update their plans based on existing commitments and then through group planning determine which project would get the resource
Exact. That's a good way of working
we'll want to see the conflicts and determine the priorities, and potentially move the work to another resource.
Once again, ProjeQtOr will not show conflicts, but delayed tasks.
I've found that I can increase the FTE on a resource
Yes
allowing me to schedule more than 1 FTE for a time period
Resource capacity is not time based : it is a fixed value valid for all durations
at the task level the system is then allowing the work effort to be scheduled up to that capacity...I..e, 40 hours in one day...etc.
Exact.

Resource with capacity of 2 represent 2 personns working : a small team into which you don't want ot differenciate persons
Is there a way to increase the FTE at the system level, but be able to restrict the resource to 1 FTE per project?
Not easily per project.

Let's take example of resource with capacity of 2 FTE.
You can :
1) Affect resource at 50% rate to project : the resource will be planned only half time "in the week". This means the work planned will be every week 2, 2, 1, 0, 0
2) Affect resource at 100% rate but assign resource at rate 50% on tasks of project. This time the planned work will be 50% of capacity every day. This means the work planned will be 1, 1, 1, 1, 1 ... on this task ... but resource could then be planned sale thing on another task of same project.
3) Affter resource at 50% rate to project AND assign at 50% rate on tasks of project. This time, the first planned task will take 1, 1, 1, 1, 1 every day, and next task on same project will not be planned (50% is already used)
Unsure I'm being clear.
You are

But I'm not sure I am
Alternatively, is there another way to approach this problem?
Yes.
1) Deal with delayed tasks.
Each project leader plans tasks. First one to plan generally books the resource capacity.
Second has delayed tasks.
If decision is to give priority to second project, priorities have just to be changed on project and both projects re-planned.
Attention, this last phase (replanning) must be done in one plannong step (with a project leader that has capacity to plan both project)
2) Deal with affectation dates : projects book resources from one date to another. This may not fit all cases but can simplify things when it's done
Regards.