Quality manual for corporation

Answer
First, ISO 9001:2015 no longer mandates the existence of a quality manual. So, organizations have a lot of freedom to decide what do they want to include if they decide to write a quality manual.
The corporation has a purpose, has a mission, each business unit work on its own way to contribute to that purpose. One of the big advantages of corporations is the synergy among different business units, like the case you mention: sharing common processes.
Start with a description of the corporation, then describe the business units and their processes and underline the existing synergies.

The following material will provide you more information about the quality manual:
How to write a short, concise Quality Manual - https://advisera.com/9001academy/knowledgebase/writing-a-short-quality-manual/
The future of the Quality Manual in ISO 9001:2015 - https://advisera.com/9001academy/knowledgebase/the-future-of-the-quality-manual-in-iso-90012015/
- Enroll for free course - ISO 9001:2015 Foundations Course - https://advisera.com/training/iso-9001-foundations-course/
- book – Discover ISO 9001:2015 Through Practical Examples – https://advisera.com/books/discover-iso-9001-2015-through-practical-examples/