How to run more than 1000 containers in parallel in AWS ECS Fargate

I need to run more than 1000 containers / tasks in AWS Fargate. As of now I have one cluster and one service. I read that this limit is for single service so I created another service hoping it would use more 1000 containers. Shall I add another cluster with ALB? or Maintain a queue ? Thanks in advance.

I am also happy if there is queue that can take one by one task with maximum of 1000 containers concurrently and then scale down to 0 where there are no tasks.