Puzzle

 ACROSS

  1 Toward the rudder

  7 Sixth sense, briefly

 10 Go well together

 14 "Neat!"

 15 Cow or sow

 16 Like pirates on the Caribbean

 17 Coaches ... or, with 18-Across, station break?

 18 Best

 19 Impudence

 20 Avg.

 21 Subway handhold

 23 Pulverized tobacco

 24 God who fell in love with Psyche

 25 The Company

 26 Get ready (for)

 29 PETA peeve

 33 Luge, for one

 34 Stingy type ... or, with 36-Across, torn down?

 36 Qualified

 37 College in New Rochelle

 38 Islamic holiday

 39 Cattle call goal

 40 Quick haircut ... or, with 41-Across, period pieces?

 41 Perfume compound

 43 What there's no I in

 44 Peacock tail feature

 46 It's nothing new

 48 Checkup sounds

 49 Tuscaloosa school, informally

 50 Beast that can weigh more than a ton, briefly

 53 '80s-'90s Susan Dey series

 54 Rap concert box

 57 Each

 58 San Francisco hill ... or, with 59-Across, split decision?

 59 Oscar winner Luise

 61 Restaurant freebie, perhaps

 62 Metal-bearing rock

 63 Amazon e-reader

 64 Doing nothing

 65 Actor Wheaton

 66 Does nothing

DOWN

  1 Anagram or sections of "Cats"

  2 Work in the mail room

  3 Croaking hopper

  4 Archie's quarterback son

  5 Dental patient, at times

  6 Questionable remedy

  7 "Como ___?"

  8 Boutique

  9 Zip back and forth?

 10 Historic document of 1215

 11 Name that rhymes with "seesaw"

 12 Narcissist's love

 13 Fair share, usually

 22 Most fibrous

 23 "Dear" one

 25 Aggressive dog

 26 ___ days (time of great success)

 27 Counting rhyme word

 28 Lump in your throat?

 29 The "F" of FBI

 30 Double-reed instruments

 31 To whom a Muslim prays

 32 Abound

 33 Locale

 35 Basic dog command

 41 Another name for Aurora

 42 Opening or closing statements

 45 Vietnamese soup

 47 State whose name ends in three vowels

 49 Tower of ___

 50 Mata ___ (World War I spy)

 51 Apple line since 2001

 52 Gallup undertaking

 53 Chicago mayor Lightfoot

 54 "No ifs, ___ or buts!"

Solution