Outies of each of the outside rows and columns yield a mass of stuff including 2 9's and an 8. Also, r8c9 reduces to {78}. If r8c9 = 8 then the 11/2 cage in n9 is (128) and the {12} of the 18/5 cage lies outside n9. That leaves {348|357|456} for inside n9 which doesn't work. So r8c9 = 7.

The 18/5 cage at the bottom right is either {12348} or {12456}. I tried {12348} and eventually reached a contradiction. So the cage is {12456}

1. Min r9c1289 = +10 -> Max r9c34 = +15
-> 24(3)r8c2 = [9{78}]
-> 20(3)r9 = {569}
Also 9 in 22(3)r6c9 in r67c9.

2. Max r9c2 = 4
-> Outies c1 -> Min r12c2 = +14(2) -> must include an 8
Since Max r1c2 = 7 -> r2c2 = 8
-> r34c1 = {79}
Also -> r19c2 from [64] or [73]
-> 10(3)n1 = {127} or {136} with (7 or 6) in r1c2
-> 1 in r9 in r9c89

3. Max r2c1 = 3 -> (Outies r1) Min r2c89 = +14(2)
-> Since 8 already in r2 and 9 already in c9 -> r2c8 = 9

4! 12(3)n7 only from [624] or [5{34}]
-> 11(3)n9 from [7{31}] or [8{12}]
-> 4 in n9 only in 18(5)
-> 18(5) from {12348} or {12456}
3 in n9 either in 18(5) or in 11(3)
But the former makes 18(5) = {12348} which leaves no solution for 11(3)n9
-> 11(3)n9 = [7{13}]
-> 12(3)n7 = [624]
-> r1c2 = 6 and r12c1 = {13}
-> 17(3)c1 = {458} with 4 in r56c1
Also 22(3)r6c9 = {589} with 9 in r67c9.

5. Remaining outies r1 -> r2c19 = +8(2) = [35]
-> r1c1 = 1
Also -> r8c8 = 5, r67c9 = {89}
-> Remaining Outies c9 -> r19c8 = +11(2) = [83]
-> r1c9 = 3
-> 12(3)c9 = {246}

6! Whichever two of (246) are in r45c9 must go in c8 in r37c8.
-> r456c8 = {17(2|4|6)}
-> 20(4)n6 = {1478} with r5c7 = 8 and r456c8 = {147}
-> r37c8 = {26}, 12(3)c9 = [4{26}]
-> r67c9 = [98]
-> r46c7 = {35}
Also 9 in n5 in r4c46
-> r34c1 = [97]
Also 20(3)r9 = [{56}9]
=> 18(5)r6c7 = [51{246}]
-> Remaining innies n8 = r79c4 = [97]
etc.

Prelims

a) 10(3) cage at R1C1 = {127/136/145/235}, no 8,9
b) 24(3) cage at R2C2 = {789}
c) 22(3) cage at R6C9 = {589/679}
d) 24(3) cage at R8C2 = {789}
e) 11(3) cage at R8C9 = {128/137/146/236/245}, no 9
f) 20(3) cage at R9C5 = {389/479/569/578}, no 1,2
g) 18(5) cage at R4C5 = {12348/12357/12456}, no 9
h) 18(5) cage at R6C7 = {12348/12357/12456}, no 9

Steps resulting from Prelims
1a. 24(3) cage at R2C2 = {789}, CPE no 7 in R12C1
1b. 24(3) cage at R8C2 = {789}, CPE no 7,8,9 in R9C12
1c. 18(5) cage at R4C5 = {12348/12357/12456}, 1,2 locked for N5

2. 20(3) cage at R9C5 = {569} (only possible combination, cannot be {389/479/578} which clash with 24(3) cage at R8C2, ALS block), locked for R9
2a. R9C34 = {78}, locked for R9 and 24(3) cage -> R8C2 = 9
2b. 24(3) cage at R2C2 = {789}, 9 locked for C1
2c. 22(3) cage at R6C9 = {589/679}, 9 locked for C9
2d. 45 rule on R9 2 remaining outies R8C19 = 13 = {58/67}
2e. 17(3) cage at R5C1 = {368/458/467} (cannot be {278} which clashes with 24(3) cage at R2C2, ALS block), no 1,2
2f. Killer triple 7,8,9 in 24(3) cage and 17(3) cage, locked for C1, clean-up: no 5,6 in R8C9
2g. Killer pair 5,6 in 17(3) cage and R8C1, locked for C1
2h. 10(3) cage at R1C1 must contain one of 5,6,7 -> R1C2 = {567}

3. 45 rule on C1 3 outies R129C2 = 18 = {378/468} (cannot be {567} because no 5,6,7 in R9C2) -> R2C2 = 8, R19C2 = [63/74]
3a. R34C1 = {79}, locked for C1
3b. 10(3) cage at R1C1 = {127/136}, no 4, 1 locked for C1 and N1
3c. 12(3) cage at R8C1 = {246/345}, no 1, 4 locked for R9 and N7
3d. 1 in R9 only in R9C89, locked for N9
3e. 1 in N7 only in R7C23 + R8C3, locked for 22(5) cage at R6C3, no 1 in R6C3 + R7C4
3f. 4 in N9 only in R7C78 + R8C8, locked for 18(5) cage at R6C7, no 4 in R6C7 + R7C6
3g. 18(5) cage = {12348/12456}, no 7
3h. 7 in N9 only in R7C9 + R8C89, CPE no 7 in R6C9

4. 45 rule on R1 3 outies R2C189 = 17 = {179/269/359} (cannot be {467} because R2C1 only contains 1,2,3) -> R2C8 = 9
4a. R2C19 = [17/26/35]

5. 45 rule on C9 3 outies R189C8 = 16 = {178/268/358/367} (cannot be {457} because R9C8 only contains 1,2,3), no 4
5a. R9C8 = {123} -> no 1,2,3 in R1C8
5b. 16(3) cage at R1C8 = {178/268/358/367/457} -> R1C9 = {1234}

6. 11(3) cage at R8C9 = 8{12}/7{13}
6a. 12(3) cage at R3C9 = {147/156/237/246/345} (cannot be {138} which clashes with 11(3) cage), no 8
6b. 8 in C9 only in 22(3) cage at R6C9 and R8C9, CPE no 8 in R8C8
6c. R189C8 (step 5) = [763/853/862/871] (cannot be [673] which clashes with 11(3) cage), no 5,6 in R1C8
6d. 22(3) cage at R6C9 = {589/679}
6e. 5 of {589} must be in R8C8 -> no 5 in R67C9
6f. R8C19 (step 2d) = {58/67}, R8C8 = {567} -> combined half-cage R8C189 = [5{67}8/658], 5 locked for R8

7. 9 in R1 only in 18(3) cage at R1C3
7a. 5 in R1 only in 18(3) cage at R1C3 = {459} or 18(3) cage at R1C6 = {459}, 4 locked for R1 (locking cages)
7b. 4 in C9 only in 12(3) cage at R3C9 (step 6a) = {147/246/345}
7c. 5 in C9 only in R2C9 and 12(3) cage
7d. 16(3) cage at R1C8 (step 5b) = [817/826/835] (cannot be [736] which clashes with 12(3) cage = {345}, only other position for 5 in C9) -> R1C8 = 8
7e. R12C9 = 8 -> 5 in C9 only in R12C8 = [35] or 12(3) cage = {345}, 3 locked for C9 (locking cages)
7f. 18(3) cage at R1C3 = {279/369/459}, no 1
7g. 18(3) cage at R1C6 = {279/369/459}, no 1

8. 45 rule on R12 2 remaining innies R2C37 = 1 outie R3C5 + 1, min R2C37 = 3 -> min R3C5 = 2
8a. 45 rule on C12 2 remaining innies R37C2= 1 outie R5C3, min R37C2 = 3 -> min R5C7 = 3
8b. 45 rule on C89 2 remaining innies R37C8 = 1 outie R5C7, min R37C8 = 3 -> min R5C7 = 3

9. 45 rule on N9 3(2+1) outies R6C79 + R7C6 = 1 innie R9C7 + 6
9a. R9C7 = {56}, min R6C9 = 6 => max R6C7 + R7C6 = 6
or R9C7 = 9, R6C9 = 9 (hidden single in C9) => R6C7 + R7C6 = 6
-> no 6,8 in R6C7 + R7C6
9b. 18(5) cage (step 3g) = {12348/12456}
9c. R8C19 (step 2d) = [58/67] -> R8C189 = [578/657] (cannot be [568] which clashes with 18(5) cage) -> R8C8 = {57}, 7 locked for R8 and N9
9d. R1C8 = 8 -> R89C8 (step 5) = 8 = [53/71]
9e. Hidden killer pair 2,3 in R7C78 + R8C7 and R9C89 for N9, R7C78 + R8C7 must contain one of 2,3, also contain 4 and one of 6,8 -> no 5 in R7C78
9f. 1,5 of {12456} must be in R6C7 + R7C6, 1,3 of {12348} must be in R6C7 + R7C8 (R7C78 + R8C7 cannot be {348} which clashes with 11(3) cage at R8C9) -> no 2 in R6C7 + R7C6

10. 18(5) cage (step 3g) = {12348/12456}, 2 locked for N9 -> R9C89 = [31], R8C9 = 7 (cage sum), R8C8 = 5, R8C1 = 6, R9C12 = [24]
10a. R1C1 = 1 (hidden single in R1), R2C1 = 3 -> R1C2 = 6 (cage sum)
10b. 4 in C1 only in R56C1, locked for N4
10c. 3 in N7 only in R7C23 + R8C3, locked for 22(5) cage at R6C3, no 3 in R6C3 + R7C4
10d. 18(3) cage at R1C3 = {279/459}, no 3
10e. 18(3) cage at R1C5 = {279/459}, no 3
10f. R1C9 = 3 (hidden single in R1) -> R2C9 = 5 (cage sum), clean-up: no 4 in R1C6
10g. Naked triple {246} in 12(3) cage at R3C9, locked for C9
10h. 1 in N3 only in R2C7 + R3C78, locked for 20(5) cage at R2C7, no 1 in R3C6 + R4C7

11. 20(4) cage at R4C8 = {1478} (only possible combination, cannot be {1289/1379/1568/2369/2378/2459/3458} because 3,5,8,9 only in R5C7), cannot be {1469/2468/2567/3467} which clash with 12(3) cage at R3C9, ALS block) -> R5C7 = 8, R456C8 = {147}, locked for C8 and N6
[Cracked, the rest is straightforward; I was surprised that this cage can only have one combination when it was the first time I looked at it.]
11a. R67C9 = [98], 17(3) cage at R5C1 = [485]
11b. R7C78 + R8C7 = {246}, locked for N7, 4 also locked for C7, R9C7 = 9
11c. R7C78 + R8C7 = {246} -> R6C7 + R7C6 = 6 = [51]
11d. Naked pair {56} in R9C56, locked for N8
11e. 18(3) cage at R1C6 = {279}, 2,7 locked for R1
11f. Naked pair {26} in R45C9, locked for C9 and N6 -> R3C9 = 4, R4C7 = 3
11g. Naked pair {37} in R7C23, locked for R7, N7 and 22(5) cage at R6C3 -> R9C34 = [87], R8C3 = 1
11h. R7C23 = {37}, R8C3 = 1 -> R6C3 + R7C4 = 11 = [29]

12. R3C2 = 2 (hidden single in C2), R37C8 = [62], R78C7 = [64], R7C5 = 4
12a. R3C8 = 6, R4C7 = 3, R23C7 contains 1 -> remaining two values in 20(5) cage at R2C7 must total 10 -> R2C7 = 2, R3C6 = 8, R3C7 = 1, R1C67 = [27]

13. R5C3 = 9 (hidden single in R5) -> R456C2 = 9 = {135}, locked for C2 and N4, R34C1 = [97]
13a. R3C2 = 2, R4C3 = 6 -> R2C3 + R3C34 = 14 = [473]

14. 18(5) cage at R4C5 = {12357} (only remaining combination), locked for N5

and the rest is naked singles.

I'll rate my walkthrough for A342 at 1.5. wellbeback's step 4 would get this puzzle a lower rating.