[name_f]Mae[/name_f] is the name me and OH like for a girl as she would honour great grandmother [name_f]Margaret[/name_f].
But thinking of a middle name is proving tricky as [name_f]Mae[/name_f] is commonly used as a MN. I tend to like family MN, but we do not have many [name_m]Long[/name_m] names in the family, and think [name_f]Mae[/name_f] would work better with a longer MN.
I can think of [name_f]Amanda[/name_f], [name_f]Gillian[/name_f], [name_f]Beatrice[/name_f] and [name_f]Florence[/name_f] from family names.
I am not keen of the flow of your family names but here are some names that would still honour your family:
[name_f]Mae[/name_f] [name_f]Betrys[/name_f] (variation of [name_f]Beatrice[/name_f])
[name_f]Mae[/name_f] [name_u]Florentine[/name_u]
[name_f]Mae[/name_f] [name_f]Florentia[/name_f]
[name_f]Mae[/name_f] [name_f]Fiorenza[/name_f]
Some names similar to your suggested middles:
[name_f]Mae[/name_f] [name_f]Clementine[/name_f]
[name_f]Mae[/name_f] [name_f]Cecilia[/name_f]
[name_f]Mae[/name_f] [name_f]Louisa[/name_f]
[name_f]Mae[/name_f] [name_f]Primrose[/name_f]
[name_f]Mae[/name_f] [name_f]Philippa[/name_f]
[name_f]Mae[/name_f] [name_f]Penelope[/name_f]
[name_f]Mae[/name_f] [name_f]Johanna[/name_f]
[name_f]Mae[/name_f] [name_f]Cassandra[/name_f]
[name_f]Mae[/name_f] [name_f]Victoria[/name_f]
[name_f]Mae[/name_f] [name_f]Susannah[/name_f]
[name_f]Mae[/name_f] [name_f]Carolina[/name_f]
[name_f]Mae[/name_f] [name_f]Jocasta[/name_f]
I really like [name_f]Mae[/name_f] [name_u]Florentine[/name_u], [name_f]Mae[/name_f] [name_f]Clementine[/name_f] (that was a contender as a first name) and [name_f]Mae[/name_f] [name_f]Louisa[/name_f].
[name_f]Primrose[/name_f] as a MN is lovely, but my sister is considering using it as a baby girls FN
As the mother of a [name_f]May[/name_f], I feel your pain! It’s a tough one to get a good flow with, but it is a lovely name. We get compliments all the time. [name_f]May[/name_f]/[name_f]Mae[/name_f] is so rarely used as a first name! I found that frillier, many-syllable names work well, as well as alliteration. We ended up with [name_f]May[/name_f] [name_f]Marigold[/name_f] ([name_f]Goldie[/name_f] is a family name), with [name_f]May[/name_f] [name_f]Magnolia[/name_f] as a close second (my favorite, but no direct family association).