is it possible to mix OM-2 with OM-3/4 Patchcords or installed Fiber. As far as i know, they are the same diameter of 50µm, they only have different bandwith caracteristics.
Is there any other reason to don't do that? (except for the orange/aqua mess in the racks ;))
If you have OM2 in the walls, it makes no difference, and if you have a mixture of OM2/3/4 in the walls, it's probably a good idea to use (only) patch cords that match the highest grade fiber in the walls, as they won't hurt the lower grade runs, though it does run a risk of making the uninformed think that all the cables in the wall are OM4 when they are not. But the uninformed are rather hard to sort out in any case.
If you have OM3/4 in the walls, it's not a good idea, though it may "work" for some value of "work." But it's a terrible place to "save" a few bucks while wasting/degrading a few kilobucks of installed fiber plant.
The rating of a cable plant is determined by the lowest rating of any link in the cable plant. If you have OM4, and you use lower rated patch cords, the rating of the cable plant is the rating of the patch cords. The same thing applies to copper cabling.
The main problem is that you are wasting your OM3/4 fiber introducing a physical bottleneck with OM2 segment. It's like the typical scenario where you have cat6 accross all the building and your users connect their workstations with cat5e.
In summary, It will work? In my experience, it works on most of the scenarios. Is it a good idea? Totally no, do it only if you have no other option.
As an additional tip, remember never mix singlemode and multimode.
