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ACROSS

 1 Oppose goal (6)

 5 Stones, for example, forming a geological layer (4,4)

 9 Call girls "cute" or "exotic" without… (10)

10 …speaking of herb that might go into the sauce (4)

11 Change damned request (6)

12 Begin as a celebrity promoter (5,3)

13 Heartlessadverse reaction (8)

15 Terminate discrimination to make one lovable (6)

17 A billionaire's marbles (6)

19 Lie down and drop leash (8)

21 French painter (an irrational skinhead) roars wildly (8)

23 Shadow or shape (6)

24 You could be grand (4)

25 Latino at sea, following tide from a European seaport (10)

26 Most of crew smell outhouse door opening (8)

27 Embrace a cult bigger than any other (6)

DOWN

 2 One typically returns to express disapproval of dessert aloud (9)

 3 Specify limb between tip of elbow and chest (7)

 4 Fabric made from piece of toxic, unwanted plant (5)

 5 Orders to cease distributing e-threads on Brazilian diplomacy? (5,3,4,3)

 6 Lay a trap in front of small percussion instruments (9)

 7 Scolded a naughty child about error outside of England (7)

 8 Country on Argentina-Uruguay border (5)

14 Suspicious ruse? Scan a guarantee (9)

16 Nazis—or an evil cohort from the Southwest (9)

18 What you need when you have a cold: time-release Sudafed (just a bit) (7)

20 Bringing up dried fruit on top of granola (7)

22 Archaic hormone containing blood of the gods (5)

23 Run with the lead in High Fidelity (5)

SOLUTION TO PUZZLE NO. 3278
 

ACROSS 1 & 3D anag. 8 anag. 9 hidden 11 NOB(OD)Y (bony anag.) 12 A + S(H)TRAYS 14 letter bank 16 2 defs. 18 ARE(N)A 20 A + RMENIA + N (Marine anag.) 23 POP + ULACE (a clue anag.) 24 anag. 27 anag. 28 letter bank 29 anag.

DOWN 1 C + OVENS 2 AER(OBI)C (care anag.) 4 init. letters 5 OPEN + SE(SAM)E 6 anag. 7 anag. 10 anag. 13 M(ON)ARCH IS M 15 S + MALL TIME 17 anag. 19 EX + PLOIT (I plot anag.) 21 A(I)RPORT (parrot anag.) 22 MOUS(S)E 25 MACH + O 26 [b]ONUS