Begin with A, B, C

Question

Across

1 A Hebrew letter
4 A franchise in various cities
7 Staggers from South Dakota
12 Muslim group in China
13 Fishy
14 Some woodwinds
15 An Oxonian college: 2 words
17 Food from the sky
18 A small but heavily studied people of India
19 Devotee
21 Occupies a throne
23 Fuss
24 Hungarian sheepdog
27 Version
30 A sausage
31 A quasibiographical play and film: 4 words
34 An unbribable federal agent
35 Where magical creatures live
36 Where to display one's stock
37 Set
38 ____ we change the clocks?: 2 words
41 Mark one's place: hyph.
44 A Hebrew month
45 Not: 2 words
48 Nerves
50 No problem: 2 words
51 Bloom County interjection
52 A string instrument
53 Keep an ____ …: 2 words
54 Piglet friend
55 A trisomy

Down

1 ____ you doin'?
2 Ancient Greek woodwinds
3 Greylags: 2 words
4 The largest public uni. system in the U.S.
5 Many an early antibiotic
6 Mag. identifier
7 An island known for its dragons
8 Auction site
9 Harry's mate
10 Appearance
11 U.S. DHS div.
16 Schmucks: hyph.
20 A Canadian ski destination
22 Home of the Salukis: abbr.
24 A dance with a partner: 3 words
25 A river in the book of Daniel
26 Parody
28 Search-by-image pioneer
29 A German mouthwash
30 Panama, for example: 2 words
31 It's used to knock down bldgs.
32 At hand
33 LL.M. alternative
37 … from the Black ____
39 Irritable
40 Jack of Twitter
41 One of the first games implicated in the game-show scandal
42 Unlocked
43 The Teflon Don got stuck on it
45 A Greek dairy brand
46 As ____ Dying: 2 words
47 A msg. received back well after it's sent
49 One way to end a boxing match: abbr.

Answer 1

That was harder than it first appeared, with several apparently contradictory answers, until I realised:

that the A,B,C of the title is a reference to musical notes, and a hint that we when we find a Solfege note name (Do, Re, Mi, etc.) in an answer, it should be entered in a single square.

The completed grid:

The answers:

1 A Hebrew letter - WAW
4 A franchise in various cities - CSI
7 Staggers from South Dakota - KERMIT (Kermit Staggers)
12 Muslim group in China - HUI
13 Fishy - SUS(picious)
14 Some woodwinds - OBOES
15 An Oxonian college: 2 words - ALL SOULS
17 Food from the sky - MANNA (... from heaven)
18 A small but heavily studied people of India - TODA
19 Devotee - FANBOY
21 Occupies a throne - REIGNS
23 Fuss - ADO
24 Hungarian sheepdog - PUMI
27 Version - EDITION
30 A sausage - SALAMI
31 A quasibiographical play and film: 4 words - THE SOUND OF MUSIC
34 An unbribable federal agent - NESS (Eliot Ness)
35 Where magical creatures live - ELFLAND
36 Where to display one's stock - TREE
37 Set - LAY
38 ____ we change the clocks?: 2 words - WHEN DO
41 Mark one's place: hyph. - DOG-EAR (turn the corner of a page)
44 A Hebrew month - ADAR
45 Not: 2 words - FAIL TO
48 Nerves - JITTERS
50 No problem: 2 words - GLAD TO
51 Bloom County interjection - ACK
52 A string instrument - UKE
53 Keep an ____ …: 2 words - EYE ON
54 Piglet friend - ROO
55 A trisomy - XYY

Down
1 ____ you doin'? - WHAT'RE
2 Ancient Greek woodwinds - AULOI
3 Greylags: 2 words - WILD GEESE
4 The largest public uni. system in the U.S. - CSU (California State University claims to be the largest, but on this page it appears below University System of Ohio.
5 Many an early antibiotic - SULFA (Sulfonamide)
6 Mag. identifier - ISSN (International Standard Serial Number)
7 An island known for its dragons - KOMODO
8 Auction site - EBAY
9 Harry's mate - RON (no idea who this is, just filled in by crossing letters)
10 Appearance - MIEN
11 U.S. DHS div. - TSA
16 Schmucks: hyph. - SO-AND-SOS
20 A Canadian ski destination - BANFF
22 Home of the Salukis: abbr. - SIU (Southern Illinois University)
24 A dance with a partner: 3 words - PAS DE DEUX
25 A river in the book of Daniel - ULAI
26 Parody - MIMIC
28 Search-by-image pioneer - TIN EYE
29 A German mouthwash - ODOL
30 Panama, for example: 2 words - SUN HAT
31 It's used to knock down bldgs. - TNT
32 At hand - HERE
33 LL.M. alternative - M.LAW
37 … from the Black ____ - LAGOON (The creature ...)
39 Irritable - NARKY
40 Jack of Twitter - DORSEY
41 One of the first games implicated in the game-show scandal - DOTTO
42 Unlocked - AJAR
43 The Teflon Don got stuck on it - RICO ("Teflon Don" is John Gotti)
45 A Greek dairy brand - FAGE
46 As ____ Dying: 2 words - I LAY
47 A msg. received back well after it's sent - LDE (Long Delayed Echo)
49 One way to end a boxing match: abbr. - TKO (Technical Knockout)