Java SE (Java Platform, Standard Edition)

I work as a PC tech at a small company and we have just transferred to an Oracle database. Our payroll department has been using ADP for years and for those of you that don't know ADP runs through Internet Explorer and requires a specific version of Java - I believe it's 1.42. Oracle is also an Internet Explorer based application and also uses Java to run, except a different version that is provided through the Oracle Jinitiator plugin. I am unsure of what version of Java Jinitiator comes with, I just know it's required and different. We have both versions of Java installed on the machine and can run the two applications separately without issues, however, we need to run them together and Internet Explorer just crashes whenever we try to launch both applications at the same time.

So pretty much is it possible to run two different versions of Java at the same time, both through Internet Explorer?

Thanks for your input!
-Doug