Challenging dependencies are usually a prioritisation problem

Big Room Planning helps align global priorities when teams have conflicting dependencies.

When teams can't complete their work within the Sprint, it boils down to just 2 things:
Things the team are in control of - such as breaking down the work into something smaller.
Things the team are not in control of - dependencies on external people and things.

Let's focus on the 2nd one, because it's the tougher problem to solve.

When your team is dependent upon other teams (or people) to complete their work, the problem is one of prioritisation. The other team (or people) has to decide their own priority of work, and that priority may not satisfy your team that has the dependency on them.

The challenge with Scrum is that it assumes encapsulation - that teams have everything they need to complete work independently. This is rarely the case which is why scaling Scrum became such a big thing over the past 20 years.

Scenario:
Let's call your team Team 1 and the team on which they have the dependency Team 2.

Team 1 makes the request to Team 2 to resolve their dependent issue. Team 2 has different priorities set by their own stakeholders or managers - the "decision maker". Team 2 ask their decision maker "what's the priority here?"

The decision maker wants to know the effort to solve the dependency, and the impact on their own priorities. Now Team 2 are pulled into understanding and estimating work that may or may not be the priority for the team.

Now there's a cost to Team 2 that impacts their capacity to determine the priority and allocation of their time.

Nobody out of the 2 teams and their respective decision-makers wants to be the bad guy by forcing their priorities, but they also don't know how to make this call. If you have very clearly defined overarching objectives that would solve this priority problem, then use that to make the decision.

What I find though is that there are always more than one "overarching objective" in any sufficiently large organisation.

This problem is one of Local VS Global prioritisation. Scrum teams have local prioritisation representing the primary goal or focus they are currently and specifically focussed on. Managers have global prioritisation where they seek to achieve longer-term objectives that requires the Scrum teams to be in alignment.

The way to solve this then is to use something like Big Room Planning:

Big Room Planning brings the two key ingredients together to address these prioritisation problems - the capacity of the teams to complete work, and the demand coming into the teams.

The "decision makers" work together in these sessions to collaborate and coordinate their priorities, and the teams work with their known capacity to schedule and prioritise work, including their dependencies, to achieve both global and local objectives.