Times 26775 - who can do this one? 28 across.
pipkirby
A general knowledge flavour to this one, I thought, with more unusual or obscure words than in recent Wednesday challenges, but all gettable with the wordplay. We uncover a cactus, an antelope, a Japanese art form, a Greek God reference, a minor book of the Bible, a Latin musical term, a kind of trousers probably derived from Kipling's India, a musical instrument ... and the name of a Greek Titan, also one of my granddaughters. When 21a went in I thought it was going to be a pangram but I can't see J or V.
I don't quite get the definition part of 11a, maybe it will come to me before I finish the blog.

Definitions underlined.

Across
1 A black horse, caught entering a monk’s office (6)
ABBACY - A, B(lack), C(aught) inside BAY.
4 Pampered head of science group in school (8)
COSSETED - S(cience), SET = group, inside CO-ED = school.
10 Arab nomad’s base in Paris or Indiana (7)
BEDOUIN - BED = base, OU = or in French, IN(diana).
11 US investigator with mobile for underground worker (7)
FROGMAN - A G-MAN was a US 'Government Man' or investigator. Then 'FOR mobile' = FRO goes in front to give FROGMAN. But a frogman is possibly an underwater worker, not an underground one? Que pasa aqui?
12 Good to abandon one form of control for another (4)
REIN - REIGN loses G.
13 Aimed, perhaps, to present integrated methods of communication? (5,5)
MIXED MEDIA - AIMED is an anagram, i.e. 'mixed' of MEDIA.
16 Draw along vessel, king having advantage (5)
KEDGE - K(ing) has EDGE (advantage). To kedge is to pull a ship along by winding in an anchored hawser.
18 Revolutionary leader initially followed by figure from east (5)
LENIN - L (leader initially) followed by NINE reversed..
19 Unresponsive, not very overbearing (9)
IMPERIOUS - IMPERVIOUS loses its V.
21 With restricted credit, encase musical instrument (7-3)
SQUEEZE-BOX - SQUEEZE = restricted credit; BOX = encase.
23 Reportedly not her expression of praise! (4)
HYMN - HYMN sounds like HIM so not HER. A fair enough homophone, unless you can pronounce the N in HYMN,as I have sometimes heard when I lived in that fine country where they often say fil-um and col-yume.
26 Work unit moving a prickly plant (7)
OPUNTIA - OP = work, (UNIT)*, A. Scientific name for the prickly pear genus, perhaps the 'punti' bit is devived from the same root as 'pointy'.
27 Academic circle sure to be taken in by mistake (7
BOOKISH - BISH = mistake, takes in O and OK = circle, sure. Perhaps academic people (or I) should be called KINDLISH now not bookish, I find it hard to read a real book these days unless it's in Big Type.
28 Pot youth leader is able to put beside cape (8)
BILLYCAN - BILL = cape, as in Portland Bill; CAN = is able. Insert Y(outh). My Dad, an Army Man, liked his billycan, I recall, when we went on camping holidays in the rain. Wiki tells me "It is widely accepted that the term "billycan" is derived from the large cans used for transporting bouilli or bully beef on Australia-bound ships or during exploration of the outback, which after use were modified for boiling water over a fire; however there is a suggestion that the word may be associated with the Aboriginal billa (meaning water; cf. Billabong). I look forward to learned input on the subject from our friends down under.
29 Bottle Geordie’s mother shows, catching large antelope (6
MAGNUM - Me MAM catches a GNU. And a-gnother gnu perhaps. It's a good few years since I heard that song.

Down
1 Cautionary signal recognised at first by doctor in A&E (5)
AMBER - MB (doctor) inside A E, R(ecognised).
2 Horse trials venue using inferior porcelain? (9)
BADMINTON - Well, bad Minton would be inferior porcelain, if there was such a thing as bad Minton.
3 Youngster consuming hot fish (4)
CHUB - CUB consumes H.
5 Leaving tip, avoiding busy periods (3-4)
OFF-PEAK - Leaving = off, tip = peak.
6 She marks Old English exercises? Cobblers! (10)
SHOEMAKERS - (SHE MARKS OE)*.
7 Little can keep yours truly subdued (5)
TAMED - TAD = little, insert ME = yours truly.
8 Manure a Welshman collected — wearing these? (9)
DUNGAREES - DUNG = manure, A, REES = Welshman.
9 Trendy pad son leaves for introduction of Oxford blue (6)
INDIGO - IN = trendy, DIG(S) = pad loses S; O(xford).
14 Prepare calmly but with sadness (10)
PLANGENTLY - PLAN = prepare, GENTLY = calmly.
15 Explosive device in writing about sick man keeping minutes (5,4)
MILLS BOMB - MS (writing) about ILL (sick), BOB (man) about M(inutes). A Mills Bomb was a kind of hand grenade introduced in 1915.
17 Orgiastic incident initiated in council upset Scotsman (9)
DIONYSIAN - SYNOD = council, reverse, insert I(ncident), add that universal Scotsman IAN.
19 Supporting old president, prohibit a craft from the Far East (7)
IKEBANA - IKE as in Eisenhower, BAN = prohibit, A. Japanese flower arranging.
20 Woman originally producing house keys (6)
PHOEBE - P(roducing), HO(use), E, B, E are keys in music.
22 Typical American university man (5)
USUAL - US, U(niversity), AL = man.
24 From Perelman, a humorous book? (5)
NAHUM - Hidden word in PERELMA(N A HUM)OROUS, 7th in order of the 12 minor prophets, book of the Old Testament.
25 Musical canon’s duty list (4)
ROTA - Double definition, one being a 'round' in music.

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