I'm not sure what your definition of "standard" is here. If it was a "standard" as in industry-standard - something from a major vendor or open-source project, it would be able to handle multiple concurrent requests; even long-running ones. Professional
J2EE apps are not only expected to support such things, they're
required to.
On the other hand if it can't run multiple concurrent requests, then it fails the basic J2EE standard. There isn't supposed to be a division between "single user" and "multi user" webapps, regardless of the language or platform. This is the kind of behaviour you get from apps that use MS-Access as their database and were the $50 low bid from Rent-A-Hacker because "IT Doesn't Matter" and "Anyone can create complex webapps, even a kid can do it!".
What you have, in short, is a carton of Chinese Pet Food. Whatever savings someone got are going to cost you an immense amount of time and money to support both initially and ongoing. You're already obligating yourself to a load-balancer that might not otherwise be needed. And Ganesh help you if it has anything to do with corporate-critical resources, because you can pretty much bet it will fail catastrophically at the worst possible moment and probably drag down other critical systems as well.
To set up multiple Tomcat instances, you need to pay attention to the differences between CATALINA_HOME and CATALINA_BASE. In common use, both these directories are the same directory. However since one refers to shareable resources and the other refers to per-instance resources, you'll have to make the distinction. Within the per-instance resources, you need to customize the conf/server.xml files to set a different set of ports for each instance.
As for managing them as windows services, at that point I have to leave you to the tender mercies of others. My own IT budget isn't up to the expense of keeping Windows servers secured, so I only work with Tomcat under Windows when clients insist. Which isn't often enough for me to keep in practice.
Some people, when well-known sources tell them that fire will burn them, don't put their hands in the fire.
Some people, being skeptical, will put their hands in the fire, get burned, and learn not to put their hands in the fire.
And some people, believing that they know better than well-known sources, will claim it's a lie, put their hands in the fire, and continue to scream it's a lie even as their hands burn down to charred stumps.