I need to configure the various department for my organization to minimize email alerts sent to operators, limit visibility to agents based on their department and enable ticket transfer through departments.

I realize that, sharing my configuration with you, I end up making a really long post 🙂 Before diving into the specific example, I'll try to summarize my needs:

I need to manage many departments;
some departments need to ask information on specific tickets to agents from other departments, but just them can respond to the user who submitted the request;
agents must be able to transfer tickets to other departments, without need to configure thier extended access to all possible departments;
only some agents (often only one email) must receive alert when tickets are transferred to their department; or I need to find another way to notify only one agent, while letting many of them have access to the ticket;
... any way to disable alerts for agents in their primary deparment?

Now, I'll explain my scenario.

A Public Relation Office (PRO) receives tickets from a public form. This office members can need to request information for ticket resolution to other agents, working in other offices. I've created the following department structure.
A main "PRO Department", with many sub-departments:

"PRO Department A references"
"PRO Department B references"
"PRO Department C references"
... and so on (I've configured 30 sub-departments this way)

PRO agents are assigned to PRO Department as primary access, and to each of the "references" department with extended access.
The reference agents from the other departments (A, B, C, ...) are assigned as primary members to their departments ("Department A", "Department B", "Department C", ...) and so on, and with extended access to their "PRO references" department. I chose this configuration to be able to uncheck alerts for some agents in the "PRO references" departments, so that only some agents in these departments receive notification when PRO agents transfer tickets to their department. Also so that references from each department don't see tickets transferred to references of other departments, while PRO agents sees everything.

You can imagine that, just stopping here, the configuration has become quite messy 🙂

Now the problem: I want to let agents start transferring tickets from any department to each other, so that Department A can transfer tickets to Department B, and so on, while limiting ticket visibility and mail alerts sent to agents in each department.
Any suggestion?
Tought about teams, but I fear I would need to create as many teams as the possible ticket tranfer options ("Team Dep A - Dep B", "Team Dep A - Dep C", "Team PRO Dep A", "Team PRO - Dep B", ...). I think that solution would be great for PRO though, because it would let its agents sharing a ticket to some agents of other departments, letting me choose who receives alerts, and letting agents from other departments post only internal notes, not replies to the users who opened the ticket.

The main problem I'd like to overcome is the need to create a configuration like "Department A - main" -> "Department A - sub", assigning the agents to "Department A - main" as primary access, "Department A - sub" as extended, just to be able to uncheck alerts in the sub department. The idea would be to assign tickets just to the sub department... But: if I let the agents see all departments, I cannot block ticket transfer to "Department A - main"; if I don't let agents see all departments, an agent without extended access to Department A cannot tranfer a ticket to this department.

Thanks in advance to anyone who will be willing to help me in any way.