Using the same page template to show one category post per page

Hi!

Here´s what I´m trying to do. I have posts which point to pages. These pages, must show a single Post Category in each. For example:
My Post “Company” points to a page named “Company” which inside, has another posts under the category “Company”. These posts are: “Overview”, “Human Resources” and “Our Offices” (all under the “Company” category).
Now, since I have another post categories, I would like to use one page template for all and not one page template per each category.
Is this possible?
Thanks in advance!