There is often the question: Different projects in a sprint - does it work? The answer is either yes or no!
Yes, it works
When you use sprints, you might use Scrum. Scrum is a framework. You take it and put the work in that frame a sprint is offering you. Once your work is in that frame, you can work on it, no matter if it you are delivering for one project or serveral. You might loose focus because the projects are tearing you apart, but as long as you are able to stabilise the priority of you work during your iteration there is chance to succeed. And you still got a ScrumMaster to support you.
No, it does not work
It will not work, if you do not put all of your work into that frame. Leaving work out of your sprint will lead to distraction and waste. Usually while there is work happening outside that is pulling your attention, this work is not weighted against the work in your sprint. There will be waste through discussions about priority and unfinished work to resume. On the other hand when there is to much ad-hoc work you will run into trouble too. Ad-hoc work is similar to work which is not framed - and yet a little bit different. A sprint is also under policy: do not disturb the people working. If your workplace produces too much ad-hoc work the process you've selected will be under constant need of maintainance, so the system will need other desire paths than your process might provide, unable to heal itself.
There is still hope
You can learn about your environment and work situation. Just make your work visible, put your work on a taskboard and follow its flow from introduction to done. Visualize the problems and impediments you encounter and improve around all mistakes that happen. It might be a hard road and it is worth it. Usually this is true: "Only what is visible can be improved."
Different projects in a sprint - it's like juggling with knives, it might work or it might hurt...