[name_f]Lily[/name_f], [name_f]Isabel[/name_f] and [name_f]Kate[/name_f] all work in their own ways.
[name_f][/name_f]Something like [name_f]Isabel[/name_f] [name_f]Marguerite[/name_f] or [name_f]Isabel[/name_f] [name_f]Frances[/name_f] or [name_f]Isabel[/name_f] [name_f]Juniper[/name_f] fits the classic-but-modern style of [name_f]Sofie[/name_f], [name_f]Charlotte[/name_f], [name_f]Clara[/name_f] and [name_f]Emma[/name_f]. This one is my favorite.
[name_f][/name_f][name_f]Lily[/name_f] is lovely and I can see it working with [name_f]Sofie[/name_f], [name_m]Max[/name_m], [name_f]Clara[/name_f] and [name_f]Emma[/name_f]. [name_f]Lily[/name_f] [name_f]Josephine[/name_f]?
[name_f][/name_f][name_f]Kate[/name_f] is good with [name_m]Max[/name_m] and [name_f]Emma[/name_f] but also with the longer names.
[name_f][/name_f]Suggestions [name_f][/name_f]-
[name_f][/name_f][name_f]Ada[/name_f]
[name_f][/name_f][name_f]Mary[/name_f] (I think this one rounds out the set very nicely at the end)
[name_f][/name_f][name_f]Marianne[/name_f]
[name_f][/name_f][name_f]Julia[/name_f]
[name_f][/name_f][name_f]Bridget[/name_f]
[name_f][/name_f][name_f]Sarah[/name_f]
[name_f][/name_f][name_f]Rosemary[/name_f]
[name_f][/name_f][name_f]Louisa[/name_f]
[name_f][/name_f][name_f]Sylvie[/name_f]
[name_f][/name_f][name_f]Eva[/name_f]
[name_f][/name_f][name_f]Eleanor[/name_f]
[name_f][/name_f][name_f]Estelle[/name_f]
[name_f][/name_f][name_f]Adeline[/name_f]
[name_f][/name_f][name_f]Abigail[/name_f] (Abigail Kate?)
[name_f][/name_f][name_f]Caroline[/name_f]
[name_f][/name_f][name_f]Evelyn[/name_f]