This can be actively managed through some enterprising Kanban and a normal Scrum delivery team method. Some agile coaches struggle with the concept that an organisation can have a single Scrum Team delivering the business change from a portfolio of programmes with multiple projects all with their own 'backlog'. Sometimes Agile methods need adapted regardless of the guidelines. I humbly suggest the following solution.
It sounds to me like you are working in a business intelligence centre/role - am I wrong?
Divide your sprint into two separate components.
- BAU Work (work outside the normal product backlog)
- Product Backlog Work (standard project work on behalf of the PM or Product Owner)
Decide how much of your sprint you are willing to sacrifice to BAU work. To help focus your delivery I suggest using the mantra
"people must be forced to make decisions."
You simply cannot deliver new change if business stakeholders continually want functionality repaired in the old system. Force people to make changes.
For this example I will suggest dedicating 20% of your fortnightly sprint capacity as BAU work.
Calculate your capacity of work per sprint in hours.
For this example we will use 3 x Full Time Resources coding for 7 hours per day for 8 days per sprint. A full day is devoted to planning and a full day to reviews and retrospectives.
That gives you an approximate capacity for 21 hours of work * 8 days = 168 hours of work capacity.
- 20% of that capacity is now earmarked for BAU work = 34 hours
- 80% of thatcapacity is now earmarked for Product work = 134 hours
Create a stack of user cards in a separate colour for the Kanban Board. These are your BAU cards. Give each of these cards a rough hours value adding to 34 and put them onto the board blank. For example: 1,1,1,1,1,2,2,2,2,3,3,5,10
Use the cards to ensure you stick to your BAU budget. Any tasks that comes into the team is given a high level planning estimate in hours and the corresponding cards is then used to track the task.
If you run out of cards for that sprint you know you have exhausted your BAU capacity.
Report on the BAU workstreams as a separate delivery report tracking the amount of hours planned and accomplished for BAU tasks including the nature of the tasks and the RoI of the work completed.