Is there a way to prevent a container from being considered 'healthy' until it has passed a certain number of consecutive successful healthchecks?

[NotSoFancyName]

I am interested in the use case when there is N successful healthchecks that puts container into healthy state.
Is there a way to achieve it?

Initially I thought that health-startup-success was serving this purpose but this field only allows to have more startup healthchecks to keep the container alive. The container is considered "healthy" as soon as the first startup healthcheck succeeds.