We like [name_u]Penny[/name_u] [name_u]Ellis[/name_u] ([name_u]Ellis[/name_u] is a family name). Our last name is three syllables, starting with with a [name_f]MAY[/name_f] sound.
I’ve always wanted to have [name_f]Kate[/name_f] in a girls name to honour someone and have been wondering - is [name_u]Penny[/name_u] [name_u]Ellis[/name_u] [name_f]Kate[/name_f] too much?
Thanks 
First of all, I love [name_u]Penny[/name_u] 
I think the rule for double middles, at least for me, is consider whether you like the middles if it was a name by itself. To clear up that really weird grammatical mess there, would you name a daughter [name_u]Ellis[/name_u] [name_f]Kate[/name_f]? [name_u]Penny[/name_u] [name_u]Ellis[/name_u] flows a lot more nicely imo, but [name_u]Penny[/name_u] [name_u]Ellis[/name_u] [name_f]Kate[/name_f] is also beautiful. Basically, yes, I’d say include [name_f]Kate[/name_f] if you’ve always wanted it.
I have to say, I am not a fan of the three-name approach. I don’t know why, but it seems kind of pretentious to me. Maybe because only royalty go for four names. And really, how many names does a kid need? Or want? Writing out so many names on official forms would get tedious. (Would they put names #2 and #3 in the “middle name” spot on official forms? Leave out name #3? Put it elsewhere? Who knows???).
All that being said, if you’re fine with the three-name thing, then as a name, [name_u]Penny[/name_u] [name_u]Ellis[/name_u] [name_f]Kate[/name_f] sounds lovely.