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Theme answers:
- 17A: Have significant influence (PACK A PUNCH).
- 26A: "Enough on this subject" ("LEAVE IT AT THAT").
- 46A: Persevere (STAY THE COURSE).
- 61A: Respond at the front (RETURN FIRE).
- 63A: "Round" thing suggested by the first words of 17-, 26-, 46- and 61-Across (TRIP).
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All of my confusion was, of course, exacerbated by the fact that I read 51D: Prime rib order as simply "rib order" and, because I had the RA in place already, entered RACK without thinking twice about it. That made the reveal answer "tcip" which I was pretty sure wasn't right. It all worked itself out eventually.
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Other crosswordese in the puzzle that we've already covered:
- 19A: Sight from the Sicilian village of Taormina (ETNA). Just yesterday!
- 2D: Algerian seaport (ORAN).
Everything Else — 1A: __ d'état (COUP); 5A: Winger of "Shadowlands" (DEBRA); 14A: Guesstimate phrase (OR SO); 15A: Fiat (EDICT); 16A: From the top (ANEW); 20A: Ali trainer Dundee (ANGELO); 21A: Sunroom (SOLARIUM); 23A: Doctrinal suffix (-ISM); 25A: Rent (LET); 33A: Starbucks order (ESPRESSO); 34A: Charm (ENAMOR); 36A: Show worry, in a way (PACE); 37A: Former California fort (ORD); 39A: Disease cause (GERM); 40A: Makes amends (ATONES); 43A: Puts in a new pot, say (REPLANTS); 49A: According to (ALA); 50A: Belgian capital (BRUSSELS); 55A: Aleve alternative (ANACIN); 60A: Superboy's girlfriend Lang (LANA); 64A: Mushrooms used in Asian cuisine (ENOKI); 65A: Elemental unit (ATOM); 66A: Places for props (SETS); 67A: Coolidge's vice president (DAWES); 68A: City NNE of Lake Tahoe (RENO); 1D: Historic NYC club, with "The" (COPA); 3D: SOS responder, often (USCG); 4D: Creep (along) (POKE); 5D: Kicks out of office (DEPOSES); 6D: Coll. dot follower (EDU); 7D: Storage containers (BINS); 8D: Pepsi competitor (RC COLA); 9D: Wheaties box picture (ATHLETE); 11D: Hostile to (ANTI); 12D: Computer list (MENU); 13D: Showed off one's butterfly? (SWAM); 18D: Kicking partner (ALIVE); 22D: Business letter abbr. (ATTN.); 24D: Sushi bar soup (MISO); 26D: Exams for future attys. (LSAT'S); 27D: Florida theme park acronym (EPCOT); 28D: Place to play (ARENA); 29D: Dodgers manager Joe (TORRE); 30D: Viking in the comics (HAGAR); 31D: Chorus from the pews (AMENS); 32D: Flourless cake (TORTE); 33D: Ecol. watchdog (EPA); 35D: Apt. parts (RMS.); 38D: Ten: Pref. (DECA-); 41D: Looks over warily (EYES); 42D: Took the wheel (STEERED); 44D: North Star (POLARIS); 45D: Greg Evans comic strip (LUANN); 47D: Treasure State capital (HELENA); 50D: Popular diner orders, for short (BLT'S); 52D: Part of ICU (UNIT); 53D: Easy marks (SAPS); 54D: Put away (STOW); 56D: A long way off (AFAR); 57D: Name as a source (CITE); 58D: Boxing's "__ Mike" Tyson (IRON); 59D: Nautilus captain (NEMO); 62D: Tiny Tim played one (UKE).