Theme: S > > > s - Take a 5-letter word that starts with an S and is still a word after you chop off the S. Repeat the resulting word, add an S and hope it makes sense. Find an appropriate clue and you're done.
17A. German cars bought by Riyadh residents? : SAUDI AUDIS
21A. Cafeteria carriers gone missing? : STRAY TRAYS
54A. Streamlined onion relatives? : SLEEK LEEKS
59A. Stories you've heard a bajillion times? : STALE TALES
10D. Out-of-tune string instruments? : SHARP HARPS
27D. Neato water sources? : SWELL WELLS
Argyle here. You could say these are rhyming anagrams with the rows overlapping and the columns intersecting. Ambitious for a Monday but complex is Erik's forte.
Across:
1. Floating platforms : RAFTS
6. Guy or fellow : MALE
10. Haughty sort : SNOB
14. Creepy starer : OGLER
15. Top military draft category : ONE A
16. Skid row denizen : HOBO. No, no; a wino or a bum but not a hobo.
19. Not many : A FEW
20. Releases (on), as an attack dog : SICs
23. QB's mishap : INT. (interception)
24. Tennis icon Arthur : ASHE
25. Makes a choice : OPTS
26. Drawing upon : USING
28. 100-yard race : DASH
30. Shoulder wrap : SHAWL
32. "Once __ a time ..." : UPON
34. PC software : APPs
38. Rose of baseball : PETE
39. Hard to hear : FAINT
40. Was a passenger : RODE
41. Figure skater's leap : AXEL
42. Uncle Remus's __ Rabbit : BR'ER
43. Nursery-rhyme Jack or his wife : SPRAT. 11D. Like Jack 43-Across's diet : NO FAT
Jack Sprat could eat no fat.
His wife could eat no lean.
And so between them both, you see,
They licked the platter clean.
44. Put down, as floor tile : LAID
46. "__ my case" : I REST
48. Fixes with thread : SEWS
50. Plastic coffee container designed for a Keurig brewer : K-CUP
51. Sports enthusiast : FAN
57. Pie à la __ : MODE. Oops. 33D. Dessert with a crust : PIE. Often made with fruit.
58. Basketball's __ "The Pearl" Monroe : EARL. Wiki
61. Bad to the bone : EVIL
62. Promgoer's concern : ACNE
63. Leaning somewhat : ATILT. An A-word but better than ALOP.
64. Lousy grades : DEEs
65. Like so : THUS
66. Zappos.com inventory : SHOES. LINK
Down:
1. Big name in vermouth : ROSSI. Martini & Rossi®
2. A second time : AGAIN
3. Vary irregularly, as prices : FLUCTUATE
4. Koppel and Knight : TEDs. One newsman on TV and one TV newsman on WJM.
5. __ Lanka : SRI
6. Teeth-and-gums protector : MOUTHGUARD
7. Conductor Previn : ANDRÉ
8. "Star Wars" princess : LEIA
9. "Piece of cake!" : EASY
12. Does as directed : OBEYS
13. Curtain call acknowledgments : BOWS
18. Part of YMCA: Abbr. : ASSN.
22. How-__: instruction books : TOs
24. Feel lousy : AIL
28. Insult comic who was a frequent Johnny Carson guest : DON RICKLES. Johnny strikes back.
Full LINK
29. Crumb-carrying insect : ANT
30. Relaxation center : SPA
31. Put a curse on : HEX
35. Financial planner's concern : PORTFOLIO
36. Handheld computer, briefly : PDA. (personal digital assistant)
37. Go down in the west : SET
39. "The X-Files" gp. : FBI. On the TV series.
43. Ninth mo. : SEP.
45. Pop the question : ASK
47. Ploy : RUSE
48. Work really hard : SLAVE
49. Spooky : EERIE
50. Reeves of "Speed" : KEANU
52. Dancer Astaire : ADELE. Fred's sister.
53. Homes for chicks : NESTS
54. Future flower : SEED
55. J.D.-to-be's exam : LSAT. (Law School Admission Test)
56. __ A Sketch : ETCH
57. Trig or calc : MATH
60. Prof.'s helpers : TAs. (teaching assistant)