Solution to 27A has been deliberately left unsolved and is to be answered only by a non-regular / novice commenter, with proper annotation. Those who have answered earlier in the week, please give others a chance.
Open for anyone to answer, if not solved by 1 PM.
ACROSS
1 Tummy in mess with dyspepsia essentially disturbing the process of neutralising foreign bodies (6,6) IMMUNE SYSTEM [TUMMY+IN+MESS+d..pEp..a}*
9 Almost all break the record (5) ALBUM {ALl}{BUMp}
10 What you do on a chess board to get cracking? (4,1,4) MAKE A MOVE [DD]
11 Opposing a gossip about popular model (7) AGAINST {A}{GA{IN}S}{T}
12 Setter calls son in difficulty (2,1,4) IN A MESS {I}{NAMES}{S}
13 Makes off with billion in a moment breaking electronic surveillance initially (8) ABSCONDS {B} in {A}{SeCOND}{Su...e}
14 Doorkeepers ignore heroin addicts (5) USERS UShERS
18 Lukewarm food getting putrid basically is rejected (5) TEPID {DI{Pu...d}ET<=}
20 Ram lives here? (5-3) SHEEP-PEN [CD]
24 Male goat's head butchered to cook porridge (7) OATMEAL {MALE+gOAT}*
26 See model drowning in drinks with senator (7) WITNESS {WI{T}NES}{S}
27 He works casually - transfer on hold on review (4-5) P?R?-T?M?R (Addendum - PART-TIMER {REMIT}{TRAP}<= - See comments)
28 Cement in free market finally moves to West (5) UNITE UN(-t)I(+t)TE
29 Excited state, perhaps? (5,7) UTTAR PRADESH {UP} Should have been 'Perhaps excited state?'
DOWN
1 I don't know the answer embarrassingly at times about British English (2,5,2) IT BEATS ME {AT+TIMES}* over {B}{E}
2 Make ends meet people to get record of past events (7) MEMENTO {MakE}{MEN}{TO}
3 To some extent, enema to determine roundworm (8) NEMATODE [T]
4 Indian state reportedly fed up with North Korean statesman (6) SIKKIM {(~sick)SIK}{KIM}
5 Egyptian Beetles injure sailors (7) SCARABS {SCAR}{ABS}
7 It's a game played in court when prison detains American on bail essentially (3,4) JAI ALAI {JAI{A}L}{bAIl}
15 Upset maid admits crime over stock again (9) REPLENISH {HELPER<=} over {SIN<=}
16 Roasted meat from lamb - Half trimmed and moderately hot, eat heartily (8) SHAWARMA {SHAved}{WARM}{eAt}
17 Maybe liqueur ingredient causes new disease eliminating drinkers finally (7) ANISEED {N+DIsEASE}*
21 Force out past ceasefire ignoring Conservative for Democrat (7) EXTRUDE {EX}{TRU(-c+d)DE}
22 Shoots old for new serials (5) SOAPS S(-n+o)OAPS
23 Keep quiet and extremely careful. Wild animal is around (4,2) CLAM UP {Ca...uL}{PUMA<=}
25 Some prophet or a telepath countered fortune-teller (5) TAROT [T<=]
Reference List
Popular = IN, Model = T, Son = S, Billion = B, Electronic = E, Heroin = H, Senator = S, British = B, English = E, Sailors = ABS, Right = R, American = A, New = N, Past = EX, Conservative = C, Democrat = D, Old = O