Greetings,
Basically, with templates built with T3 framework (like Purity III), to build up a page, it will relate to Template style, Layout and menu item.
For Corporate page in Purity III, you will need to:
1) Create ‘Corporate’ template style under: Extensions > Templates
2) Open this style, assign ‘corporate’ layout to this template style via ‘Layout’ tab
3) Create menu item, in your case, it’s home menu item.
4) Assign ‘Corporate’ template style you just created to the home menu item.
Check out this guideline for which positions are included in this layout, then assign your desired modules to associated positions as you wish: https://www.joomlart.com/documentation/purity-iii/layout-in-details#corporate-layout
Hope this helps.
Cheers!