It sounds like you've moved more towards operations than project management, but I could be wrong. Either way, the same concepts apply. There's no rule or restriction, as each PM is different. It just depends on your own management style and how comfortable you feel. It goes to David Espina's Span of Control comment.
At various times, I've managed 20-25 projects with 5 reports, and others it was 40+ (plus general operations) with 9 reports. Managing them directly, it would be about half that. The more projects, the more hands-off I became and relied on the reports to do their job and provide me with the information I needed. For example, at one point I was responsible for all the projects in our division, but also I was responsible for the accounting (A/R,A/P). Accounting isn't my area, so I had an Office Manager that handled that and provided me with weekly status reports so I could watch for and deal with problems at a division level.
A big part of it isn't dollar volume, or number of tasks or projects, but management complexity. If your projects are relatively straightforward from a management standpoint (limited # of stakeholders or they're the same for every project, limited importance to the co., similar work, etc) then you could probably do more than if they were complicated.
From your description I would say you're in a somewhat complex environment as each of those depts you listed are going to have differing goals. So the complexity of managing increases because, as a whole, they're pursuing the same goal (product success & growth), but as depts they're chasing different ones, and they don't always work in parallel. So I would say you're perfectly justified in asking for assistance.