For boys, I’d put a bet on [name]Arthur[/name] or [name]Phillip[/name] – they’re [name]Charles[/name]’ middle names too, so they could reasonably make it in there somewhere, though probably not together.
You might also expect to see a [name]David[/name] – it’s one of [name]Harry[/name]'s middle names, and given [name]William[/name]‘s attachment to Anglesey, naming a son after [name]Wales[/name]’ patron saint seems plausible.
[name]Albert[/name] and [name]George[/name] have been in the fam for ages, so one of those might pop in, though again, probably not both at once – a bit oldy-moldy in large doses.
Dark horse is [name]Francis[/name] – middle name of [name]Kate[/name]'s father and [name]Prince[/name] Consort [name]Albert[/name]. [name]Diana[/name]'s mn was [name]Frances[/name].
Likelies:
[name]Edward[/name] [name]Arthur[/name] [name]Patrick[/name] [name]George[/name]
[name]Phillip[/name] [name]Albert[/name] [name]Frederick[/name] [name]Louis[/name]
[name]Henry[/name] [name]Phillip[/name] [name]Louis[/name] [name]Charles[/name]
Less-likelies:
[name]Arthur[/name] [name]Phillip[/name] [name]Christian[/name] [name]Edward[/name]
[name]David[/name] [name]Albert[/name] [name]Henry[/name] [name]George[/name]
[name]Charles[/name] [name]Francis[/name] [name]William[/name] [name]Andrew[/name]
For girls, there isn’t as much variety as for the men, but you’ll almost surely see an [name]Elizabeth[/name], as [name]Kate[/name]'s middle name and the Q’s first name. I think [name]Alexandra[/name] will work her way in. It is QEII’s middle name, [name]Alexandrina[/name] was [name]Queen[/name] [name]Victoria[/name]'s first name, and it’s still contemporary-sounding.
[name]Don[/name]'t count out [name]Louise[/name], though it’d likely be a middle name owing to Lady [name]Louise[/name] of [name]Windsor[/name].
Dark-horse, let’s throw [name]Charlotte[/name] in there – no royal ladies have used this in a while, and it’s a tribute to [name]Charles[/name] (if you’d want to do that sort of thing )
[name]Elizabeth[/name] [name]Anne[/name] [name]Mary[/name] [name]Louise[/name]
[name]Alexandra[/name] [name]Elizabeth[/name] [name]Alice[/name] [name]Victoria[/name]
[name]Charlotte[/name] [name]Mary[/name] [name]Catherine[/name] [name]Louise[/name]
[name]Mary[/name] [name]Catherine[/name] [name]Elizabeth[/name] [name]Mary[/name]
[name]Victoria[/name] [name]Augusta[/name] [name]Mary[/name] [name]Elizabeth[/name]