One missing bit is technically one product (for example, one code base, even if large) or not.
If these are completely separate products , then using Scrum, I would go for very short sprints (1-2 weeks) and work on developing a sequence. So two weeks of project A, then project B, then C, then again A - maybe for two sprints, then C, etc. In such a situation, a single lag does not make sense, separate blocks must be stored for A, B and C. I know at least one command that works like this.
If you need more software, it is rather a function of product knowledge. Maybe you need someone for each project, maybe you have someone who knows A, B and C well to be a PO.
If there are different products, then when you try to do this by accepting different stories from different magazines, each sprint in which you end up is a divided team. Naturally, people will specialize in this project, it will also be very difficult to have a good definition (we do it if we can send new increments for A and B, but not C with this sprint?). If you cannot organize projects with short sprints, I would look at Kanban, trying to invest some kind of organization in it.
If this is one product / one code base , then everything is much simpler. Even if the team has to touch different areas of the code base due to different projects, they will still work on the same products, so all Scrum mechanics will be well applied. One lag, one software.
One drawback to this should be noted is that the people on the team will switch to the context, and there is a penalty from this, no matter what process you use. Whatever process you choose, you should try to minimize this as long as possible (as long as the business can hold on). The good thing about Scrum is that it has this built-in agreement with PO that context switches can only happen at the sprint border - in other words, the team will get 1-2 hours to concentrate before switching to another project.
In addition, do not forget about all the technical practices of flexible work. Unit tests. Automated builds and tests. Code Review. Smart use of repositories. High standards. qualitative. All this is necessary in such a complex environment.