Technically, yes, it's quite possible. Realistically, it depends on a number of variables.
To answer the last part of your question first, it's unlikely that you would be able to run VA applications from different developers on the same camera at all. And even if you *could*, I would personally avoid it, as the risks and troubleshooting difficulties would likely make you regret the decision.
On our cameras (Avigilon), we currently focus on object-classification analytics, where the system can identify (eg: classify, not identify as in saying "This person is Bob") people and vehicles in motion in the scene.
The rough logic flow in our camera is that objects are classified BEFORE any rule consideration, we attempt to classify any moving object as a person or vehicle (or, ignore it if it doesn't look like what we would expect, eg: a dog, or a shadow). Once the object is classified, the rules engine is consulted to say "is this object breaking one or more rules?".
This approach allows you to run multiple kinds of analytics rules simultaneously, because the hard part (object classification) is handled separately from the rules part. You can have a tripwire in one part of the of the field of view, a loitering rule in another, and an object present in region in another area. However, it's not very common for people to run multiple rules types, they usually just end up using "object present in region", as that tends to work best overall for the standard security application.
For any analytics scenario, you need to think more about the FOV and camera placement/coverage to give the best possible view to the analytics algorithm. For this reason, a camera deployed for face rec is going to have a much different FOV than a camera deployed for loitering (a more straight-on shot, usually at a choke point area vs. a higher up overhead shot).
Given the wide variety of analytics options available in the market (in terms of performance, practical coverage area, resolution, etc.) I would personally recommend not trying to find one "do it all" solution right now, but instead prioritize your needs and find the right tool for each job. Pay attention to what it takes to setup/tune the performance and to maintain that performance over time. Investigate integration options with your VMS of choice and how alarms are brought into the VMS, automation flexibility, and so on. Also, be sure that you can do a real-world test of the performance in YOUR environment, don't rely just on demo videos or spec sheets. Pay attention to daytime vs. night time performance and coverage area/range. Test false alarm immunity by not just concentrating on "does it catch a person" but also "does it ignore the proper things".