OK, I got this messed up as I only shared DS result with Pate.

DS ranked 405 / All Pupils. Any chance on waiting list post-March 1st at Tommies (STR)? Thanks for looking!

Unfortunately, you have to have indicated in advance that you want to have your DC's raw score standardised with the cohort for a particular school. From the info sheet on the STR website:

What happens if I am interested in more than one Grammar School?
If you are also considering Marling, Pate’s or The Crypt School you must include this information on your registration form but indicate at which school you wish to take the test. This should be at the school which is likely to be your highest ranked preference. All four schools sit the same test at exactly the same time. The test results will be shared between schools and your son will be included at the appropriate place in the rank order for each school, irrespective of where your son has taken the test.

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Outside of a dog, a book is a man's best friend. Inside of a dog it's too dark to read.Groucho Marx

Does this mean can't gon on the waiting list after March 1 for subsequent allocation?

Looking at the Admission Policy, there is scope for being added to the waiting list through sitting the late test in March, so possibly at this point there is the facility for having one's raw scores standardised with the school's cohort if you have taken the test at the normal time but not shared? There is nothing explicit about this in the policy, though.

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Outside of a dog, a book is a man's best friend. Inside of a dog it's too dark to read.Groucho Marx

I suggest you call the school and ask.

Perhaps the first move would be look for a comprehensive school that's close to home?