|Images sources: line 1: images 1, 4, 5: Jurgen Appelo; image 2: Caren Calhoun; image 3: Brenda Do;
line 2: image 1: Chip Houston; image 2: Bernd Geropp; image 3: Jurgen Appelo; image 4: Leadership Link.
A quick hit  research with the phrase [delegation levels] shows variety of patterns, with 4, 5, 6, 7, 9 or 10 "delegation levels".
4 levels : Chip Houston (Andy Stanley with Gavin Adams)
5 levels : Michael Hyatt (Michael Hyatt)
5 levels : BillZippOnBusiness (Bill Zipp)
5 levels : Discwizardonline (Nancy Roberts)
5 levels : Discipleship (Eric Gallagher)
5 levels : Greendoor Virtual (Brooke Simmons / Sarah Gibson)
5 levels : Strong-Bridge Consulting (Heather Mier)
5 levels : ANZ Business Growth Program (University of South Australia)
5 levels : Inc.com (Peter Economy)
5 levels : Quantum Learning Solutions (Susan Cullen)
6 levels : University Lake School Leadership Development Programme (Karen Calhoun)
6 levels : Bizcatalyst 360 (Tim Crocker)
6 levels : attribution under progress (temporary Google research with "6 levels of delegation")
6 levels : forbes.com/sites/ (George Bradt)
7 levels : Management 3.0 (Jurgen Appelo)
7 levels : Evan Carmichael (Martin Haworth)
7 levels : Upwork (Brenda Do), based on Businessballs
9 levels : original paper / book not identified yet (Sir Tim Brighouse)
10 levels : Businessballs 
How many delegation levels would you institute to increase agility of your digital systems ?
What if, from your company culture and change management perspectives, you replace the notion of delegation level by the notion of delegation regime ?
For IT/digital operations, Tru Do-Khac has created the framework "IT Regime Management", which is articulated around the notion of governance regime.
 As a matter of fact, not so quick : under the business & professional loyalty imperative of the digital era, we made our best efforts to reference under the conditions
- there is a clear attribution to identified professionals with simple facilities to contact, possibly in view to confirm fair use under commercial or professional context
Update March 21. 2018
Two other delegation levels patterns, inspired from automation levels for automotive vehicles