I’m really liking your shortlist! @megan33
Here’s what I liked:
Alice
Alexandra (what are your favorite nn?)
I don’t really do NNs but Sascha/Sasha is very common in Russia.
Theodora
Arabella
Rose
Philippa
Mary
Marguerite
I’m pretty sure 1-2 of your full name choices were selected for Queen Victoria’s many children.
First of all, I think [name_m]Henry[/name_m] and [name_f]Mary[/name_f] sound too similar…
Seems as though the names you’d like in your combo are [name_f]Mary[/name_f] and [name_u]Louise[/name_u], and either [name_f]Philippa[/name_f] or [name_f]Alexandra[/name_f]. Of your combos I like [name_f]Philippa[/name_f] [name_f]Mary[/name_f] [name_u]Louise[/name_u] and [name_f]Alexandra[/name_f] [name_f]Mary[/name_f] [name_u]Louise[/name_u].
First names that I think go best with [name_f]Frances[/name_f], [name_f]Eleanor[/name_f] and [name_m]Henry[/name_m] on your list are [name_f]Amelia[/name_f], [name_f]Alice[/name_f], [name_f]Alexandra[/name_f], [name_f]Rose[/name_f], [name_f]Philippa[/name_f] and [name_f]Louisa[/name_f].
Other potential first names to consider:
[name_f]Annabel[/name_f], [name_f]Beatrice[/name_f], [name_f]Caroline[/name_f], [name_f]Charlotte[/name_f], [name_f]Clementine[/name_f], [name_f]Constance[/name_f], [name_f]Georgina[/name_f], [name_f]Matilda[/name_f].
A few combo suggestions:
[name_f]Alice[/name_f] [name_f]Mary[/name_f] [name_u]Louise[/name_u]
[name_f]Annabel[/name_f] [name_f]Louisa[/name_f] [name_f]Mary[/name_f]
[name_f]Beatrice[/name_f] [name_f]Mary[/name_f] [name_u]Louise[/name_u]
[name_f]Caroline[/name_f] [name_f]Alexandra[/name_f] [name_f]Rose[/name_f]
[name_u]Louise[/name_u] [name_f]Alexandra[/name_f] [name_f]Mary[/name_f]
[name_f]Matilda[/name_f] [name_f]Philippa[/name_f] [name_u]Louise[/name_u]
[name_f]Philippa[/name_f] [name_f]Louisa[/name_f] [name_f]Rose[/name_f]
Honestly anything then “Mary Louise” goes beautifully!
Oh I love [name_f]Matilda[/name_f] and Caroline!! They’re both added to the list 
I also really like [name_f]Clementine[/name_f], but am afraid it is a little too unique for [name_f]Frances[/name_f], [name_f]Eleanor[/name_f], and [name_m]Henry[/name_m].
Thank you so much 
[name_f]Glad[/name_f] to hear!
[name_f]Alice[/name_f] goes perfectly imo! [name_f]Louisa[/name_f], [name_f]Philippa[/name_f], and [name_f]Rose[/name_f] also work 
[name_f]Alice[/name_f], [name_f]Philippa[/name_f], [name_f]Louisa[/name_f] and [name_f]Mary[/name_f] are my favourites for you! I especially like [name_f]Philippa[/name_f] [name_f]Mary[/name_f] [name_u]Louise[/name_u] as a combo! [name_f]Alexandra[/name_f] and [name_f]Mary[/name_f] together are a little too royal imo (the Queen’s full name is [name_f]Elizabeth[/name_f] [name_f]Alexandra[/name_f] Mary) but I don’t think it’s a big deal.
Some nickname ideas for [name_f]Alexandra[/name_f]:
[name_u]Allie[/name_u]
[name_u]Alex[/name_u]
[name_u]Lex[/name_u]
[name_f]Lexa[/name_f]
[name_u]Lexi[/name_u]
[name_f]Xandra[/name_f]
[name_u]Andy[/name_u]
[name_f]Annie[/name_f]
[name_f]Anna[/name_f]
[name_f]Anya[/name_f]
i like amelia, alexandra, isobel, cecilia, rose and philippa (especially w the nickname poppy) with frances, eleanor, & henry!! i also love the combo alexandra mary louise!!
other ideas:
amelia isobel rose
alexandra rose louise
isobel theodora mary
cecilia louise mary
rose alexandra louise
philippa theodora alice
arabella rose louise
mary alexandra rose
frances, eleanor, & henry are lovely together! here are my thoughts on your list…
amelia–i love this, and i think it fits in perfectly with your sibset.
alice–same as amelia! although i think i prefer amelia with your set to avoid repeating ending sounds with frances.
alexandra–i’m not a fan, but objectively i can appreciate the appeal. i love annie for a nn!
isobel–same as alexandra, although i like this better.
theodora “teddy”–i love teddy, but i’m not too keen on theodora. i love the similar dorothea, though!
augusta “gussie” or “aggie”–i adore august, but for some reason i’ve never quite gotten on board with augusta. it feels a tiny bit stuffy to me. aggie (or auggie?) is very cute though!
arabella–this gives me very princessy vibes! i don’t love it, but it’s definitely pretty and i can see the appeal.
cecilia–i really like this! it gives me a slightly different vibe than the rest of your sibset, but i can’t pinpoint why; overall, i think it fits nicely.
alberta “bertie” or “birdie”–i prefer the nicknames here over the full name, but i do think the full name works well with the sibling names.
rose–a lovely, can’t-go-wrong classic.
philippa “poppy”–philippa feels a bit overly serious to me, but poppy definitely injects it with a bit of fun, lighthearted energy! i like pippa too.
louisa–i love love love this, and i think it fits perfectly with your trio!
mary–another that i love and that i think fits really well.
marguerite–i like, but don’t love, this. i prefer margaret and marjorie.
overall my favorites for you are louisa, amelia, mary, alice, and cecilia, in roughly that order!
louisa mary alice
amelia marguerite rose
mary alice amelia
alice arabella poppy
cecilia augusta mary