To understand your team's needs you need to go beyond engagement-survey scores. Study the comments to see the reason behind dissatisfaction.
Provide feedback-channels for employees to submit rich open-ended text feedback about daily teams frustrations and encountered issues on the job.
Let your team verbalize their daily job experience. Topics might come up you wouldn't have thought to ask for in a structured survey.
Discuss the collected feedback together in the team and devise solutions together to demonstrate that feedback is valued.