The Book of Night with Moon/Feline Wizards series is a sister series to Young Wizards, also written by Diane Duane, following the adventures of a group of wizardly cats who maintain the worldgates in New York City. Currently there are three books: The Book of Night with Moon, published in 1997, To Visit the Queen, published in 1999, and The Big Meow, written as a Storyteller's Bowl project but not "officially" published yet and currently available only via "subscribing" at the project web site. The series is targeted to adults instead of a Young Adult audience, but the only difference this makes is the presence of some explicit references to sexuality and the fact that the viewpoint character, Rhiow, is an adult cat.
These books provide examples of:
Alternate Timeline: One pops up in the second book and the plot revolves around stopping it from overwriting the protagonists' timeline.
Call a Rabbit a "Smeerp": There's a fair amount of it, between the use of cats' words for familiar things (like houff for "dog") and the mangled versions of human names for other things (cats aren't really equipped to pronounce most consonants).
Cats Have Nine Lives: They reincarnate eight times, keeping their personalities and some but not all of their memories. A cat can feel what life they're on, and the subject of how many lives one has left is fairly personal, something it's okay to divulge but not okay to just brazenly ask about.
Chess Motifs: The cats have their own strategy game depending on position, ownership of people and things, etc.
Fictionary: The important words in Ailurin (some of which have simple translations, but most of them don't) are untranslated, with a glossary provided at the back of the book.
God of Evil: While the Lone Power is as much the enemy as in Young Wizards and in much the same way, cats don't seem to separate Her out from the other Powers quite as much as humans do. She's a goddess to them - one whose work and desires need to be opposed at all costs, but a goddess to be reunited with the pantheon, not the Devil.
The cats are basically a society of these; they're as cognitively capable as humans, but they don't think like humans. They're also physically incapable of building much of anything and normally speak their language at a volume inaudible to humans, which mostly explains why humans aren't aware that cats are that smart.
Many other species are said to be this, and can produce wizards; canine and falcon wizards are discussed, but not shown.
Masquerade: Not from other cats, but they make up for it with extra worrying about humans. Notably in the second book, while planning a commuting schedule: Rhiow (who's living with a human) asks Arhu (who she knows isn't) whether there are any humans, anywhere he visits, who take special notice of him and might worry if he didn't turn up regularly. People can go to surprising lengths when a cat goes missing...
No Biological Sex: Though they have gender identities, spayed or neutered cats are treated as basically this by cat society.
The books state they the words "queen" and "tom" not just to differentiate from this but because "female" and "male" don't accurately portray just how important the distinction is to cats, who do after all go into heat. The narrator being a female spayed in kittenhood makes her viewpoint on same- and mixed-sex relations unusually humanlike... both for better (her viewpoint's more audience-relatable) and for worse (she tends to fail to notice or entirely misread subtext).
Of the People: The cats' name for their species is People. They don't actually call other species "not-people", though. They look down on humans somewhat (in a patronising way, rather than a xenophobic way), but not as much as they look down on dogs, birds, rats, and other animals that are either prey or competition for cats.
Oracular Urchin: Arhu develops into one, although his personality remains fairly down-to-earth.
Starfish Language: Ailurin qualifies from a human perspective, though there are at least two humans who learned to speak it anyway. It's a tonal language with 37 vowels, extremely sensitive to mispronunciation. The transcriptions are both rather approximate and condensed to be more accessible to the human audience. Also, what cats consider normal volume is inaudible to humans; to be heard by a human they have to shout. (This goes both ways: most human attempts to talk back to "their" cat(s) comes across as yelling in Hulk Speak and/or a horrible accent.)
The bit about volume is a little Truth in Television; cats really do have extraordinary hearing, and they can easily pick up a quiet sound from halfway down the block.
And "shout" also refers to body language, which supposedly makes up a lot of what's being given as dialogue.
Steam Punk: The alternate timeline from the second book is a pretty textbook case. But they have nukes, which they first use to Deface of the Moon and then to blow themselves up in the 1880s.
Stuffed into the Fridge: The Lone Power arranges for Rhiow's owner Hhuha/Susan to get hit by a taxi in the first book, to distract her with grief and discourage her from interfering.
Timeline-Altering MacGuffin: From the second book, Van Nostrand's Scientific Encyclopedia, a massive book dropped by an unfortunate London student who was briefly diverted into the year 1874. It contains pretty much all the information about modern science and technology you could possibly need.