We applied to 9 last year (yes, bonkers!)
We are in London and DD is in state primary whose ofstead rating switches between 'requires improvement' and 'inadequate'.
We were preparing her ourselves at home starting year 5 and we had absolutely no idea where she stood relative to her peers.
In the absence of any useful information from school, we applied for three very selective schools (likes of Henrietta Barnet, CLSG etc), four relatively less selective (SHHS and similar), and two with broader intake.
At the end, she didn't receive offer from any of the super-selectives, but received offers from most of the rest. So it sort of worked out.
If we had more information about her relative position among peers, like what prep schools and most professional tuition classes give, we would have probably applied to four, or at most five (one dream school, two middle of the road, two safer options).
We didn't take daughter to visit all the schools though, only three schools where I thought she had better chances. I visited all nine 😣