Scrum team of 17? Is that possible?

s there any way Scrum would allow or even recommend such big teams?

Recommended or allowed? No.

That doesn't means it doesn't take place in many organizations. I have had a similarly-sized team work for a single Product Owner. That was quite cumbersome, but the Scrum Team was focused around sprint work and Sprint Goals. This dynamic can still technically follow Scrum, although team size will remain an issue.

I have also had a large team serving multiple Product Owners, similar to your situation. Unfortunately this creates a fragmented view of work, and simply isn't Scrum. There are benefits to visually identifying and tracking work, but with multiple PO's, it is near impossible to create any sense of team ownership of sprint stories, or identify a Sprint Goal.

Look to the 5 Scrum values (Focus, Openness, Respect, Courage, Commitment) and see how your setup either supports these values, or contradicts these values. Use your observations as a good starting point for discussion if things are not working.

Good luck.

You need to sort out who the product owner is first. If there is a single product, or a composite one with a clear value stream, then you may need a Nexus of teams with one PO. The act of combining the teams might have been a bodged attempt at doing something along those lines, but which left product ownership unresolved.

If your current POs represent separate products and unrelated value streams then we should expect separate and unrelated teams, but if that was the case then (I suppose) they would not have been combined in the first place.

Always go to the source: http://scrumguides.org/scrum-guide.html

Having three to four Product Owners is a violation.

There is no rule that there can only be three to nine Development Team members. Some reasons are given for each of these recommended size constraints.

The biggest problems I've encountered with a large team were communication, coordination, and knowledge sharing.

Sounds to me whoever had input into the reorg were not aware or concerned with Scrum at all. That is usually the case when there is not top down understanding and buy in. If "the team" truly wants to implement scrum they may have to revisit roles if possible and organize a team(s) with in the team but my guess is there are large issues here that will always cause a problem unless resolved by those who own the problems.

Just a thoughts...

If there are 3-4 product owners, why not to break team based on some functionality into 3-4 cross functional teams? Each team will have single PO, single sprint goal, separate SBI while share PBI, DOD and even SM.

Maybe they choose to have only one big Scrum Team to help priotitize at the product-portefolio level, in order to focus at one time on the more valuable product ?

But if each Sprint is made of a mix of tasks from the 4 products, your suggestion really make sense to me.