Scarification / Moss Control...Please Advise

grass

Hi,

I sprayed moss patches on my lawn with soluble iron sulphate. This blackened / killed the moss quickly. 

Thinking most/all of the moss was dead, I scarified on a medium setting (first time in 20 years). The grass looks thinner and less green but still very established.

With the grass thinner, I'm still seeing moss patches. I'm planning to spread an iron sulphate fertiliser to thoroughly dispatch of any remaining moss. Following this, the easiest way to remove the black moss is to scarify again in a couple of weeks. 

My question, is it safe to scarify the lawn again? should I reduce to a lighter setting? 

Any advise on moss killing and lawn recovery is much appreciated.

Thanks, Jonathan

Firecracker

I would scarify again, then over seed with a top dressing. In fact that is what I am doing in parts of my lawn.