In a team conference, I asked this question to my multilevel support team:
How do you solve a Support issue?

Our most experienced Support Engineer piped up: “One at a time!”
In our discussion, we explored that idea.

It’s true because each issue has unique aspects and details that need to be understood. It’s also true because we need to focus on a specific problem to solve it and avoid time consuming context switching. And it’s also true that no single troubleshooting approach fits all problems.

Some issues need swarming or pair troubleshooting, others can be handled by an individual going deep. Some issues fall into well-known categories and others are totally unique. All issues are attached to a user and customer, so deserve our undivided attention to ensure good service and communication.
Some issues need escalation to the Product team, so systemic problems get addressed.

It is also true that if you spend your day running through your case queue and never settle in to definitively solve issues, you will not make progress.

However reviewing your queue at a high level with your manager or another engineer is essential. The high-level review is useful for setting priorities, establishing troubleshooting approaches, picking out problems that need escalation or special handling and identifying easily solved low hanging fruit.

Part of the art of delivering support is intelligently adapting the problem-solving approach to the particular issue.