Question about responsibility and role

We have defined that we need to create a custom responsibility for Engineer. This custom Engineer responsibility will be able to access to functions and submenus under inventory responsiblity, bills of material responsibility, WIP responsibility and supply chain planner responsiblity. I did end up created a custom menu to combine all four responsibilities together. However, when I assign this menu to the Engineer responsibility, which application should I put under the data group and request group? All four responsibility came from four different applications. Or, is this way even possible to do? Please advise. If this is not possible, and