This puzzle is essentially a jigsaw killer with gaps to place the killer cage totals, in kakuro style. Since there are 11 rows and columns I’ve labelled them 1 to 9, then A and B. Jigsaw nonets have been identified by their upper left-hand cells.
Initial Placements.
a) 45 rule on R5 1 innie R5CB = 8, placed for NR3C8
b) R5CB = 8 -> R34CB = 14 = {59}, locked for CB and NR3C8
c) 45 rule on R7 1 innies R7C1 = 5, placed for NR7C1
d) 45 rule on C5 1 innie R8C5 = 6, placed for NR4C5
e) 45 rule on C7 1 innie R4C7 = 8, placed for NR4C5
Prelims, taking account of initial placements, with direct results.
a) R1C12 = {19/28/37/46}, no 5
b) R1C45 = {19/28/37}/[64], no 5, no 4 in R1C4
c) R12C7 = {16/25/34}, no 7,9
d) R2C9A = {17/26/35}, no 4,8,9
e) R3C12 = {13}, locked for R3 and NR1C1, clean-up: no 7,9 in R1C12
f) R5C89 = {12}, locked for R5 and NR3C8
g) R7C34 = {17/26}
h) R9CAB = [86], both placed for R8CA
i) RAC12 = {18/27/36/45}, no 9
j) RABC5 = {19/28/37}, no 4,5
k) RBC78 = {49/67}/[58], no 1,2,3, no 5 in RBC8
l) RBCAB = [47/74/92], RBCA = {479}, RBCB = {247}
m) 19(3) cage at R3C4 = {289/469/478/568}
n) 10(3) cage at R9C6 = {127/145/235}, no 9
o) 19(3) cage at R9C2 = {289/379/469/478/568}, no 1, clean-up: no 8 in RAC3
1a. Naked triple {467} in R3C89A, locked for R3 and NR3C8 -> R4C9 = 3, clean-up: no 5 in R2CA
1b. 19(3) cage at R3C4 = {289} (only remaining combination), locked for R3 and NR1C4 -> R34CB = [59], clean-up: no 1 in R1C45
1c. 1,5,9 in R1 only in R1C789AB, locked for NR1C7, clean-up: no 2,6 in R1C7, no 7 in R2C9, no 3,7 in R2CA
1d. Naked pair {26} in R2C9A, locked for R2 and NR1C7, clean-up: no 1,5 in R1C7
1e. Naked pair {34} in R12C7, locked for C7 and NR1C7, clean-up: no 9 in RBC8
1f. Killer pair 3,4 in R1C45 and R1C7, locked for R1, clean-up: no 6 in R1C12
1g. Naked pair {28} in R1C12, locked for NR1C1, 8 locked for R1
1h. R1C4 = 6 (hidden single in R1) -> R1C5 = 4, placed for NR1C4, R12C7 = [34]
1i. R7C3 = 6 (hidden single in NR6C1) -> R7C4 = 2, placed for NR7C1, clean-up: no 3 in RAC2
1j. Naked triple {579} in R2C123, 5,7 locked for R2 and NR1C1 -> R2C6 = 8
1k. Naked pair {13} in R2C45, locked for NR1C4
1l. Naked pair {57} in R45C4, locked for C4
1m. Naked pair {46} in R4C12, 4 locked for R4
1n. 1,3 in RB only in RBC12345, locked for NRAC2, clean-up: no 6,8 in RAC2, no 7,9 in RBC5
1o. 19(3) cage at R9C2 = {379/478} (cannot be {289} which clashes with R1C2, cannot be {469} which clashes with R4C2, cannot be {568} because no 5,6,8 in R9C2), no 2,5,6, 7 locked for C2, clean-up: no 4,7 in RAC3
1p. 7 of {379} must be in RAC2, 8 of {478} must be in RBC2 -> no 4,7 in RBC2
2. 3,4 in NR4C5, only in R5678C6, locked for C6
2a. 2,5 in R9 only in 10(3) cage at R9C6 = {235} -> R9C8 = 3, R9C67 {25}, locked for NR7C8, clean-up: no 8 in RBC8
2b. R8C13 = {38} (hidden pair in NR7C1), locked for R8
2c. 8 in NR4C3 only in R6C2345, locked for R6
2d. R7C9 = 8 (hidden single in NR6C7)
2e. RAC8 = 8 (hidden single in NR7C8), clean-up: no 2 in RBC5
2f. 4 in NR7C8 only in R78BC8, locked for C8
3. RAC6 = 6 (hidden single in C6), placed for NRAC2
3a. 6 in RB only in RBC78 = {67}, 7 locked for RB and NR7C8, clean-up: no 4 in RBCAB
3b. RBCAB = [92], both placed for NR8CA
3c. RBC3 = 5 (hidden single in RB), RAC3 = 2 -> RAC2 = 7, RAC5 = 9 -> R8C5 = 1, R2C45 = [13], RAC7 = 1, placed for NR7C8
3d. Naked pair {49} in R78C8, 9 locked for C8
3e. R8CAB = {17} (hidden pair in NR8CA), locked for R8
3f. Naked pair {17} in R18CB, locked for CB
3g. R2C2 = 5 (hidden single in R2)
3h. 2 in R4 only in R4C56, locked for NR4C5
3i. R8C9 = 2 (hidden single in R8), placed for NR6C7, R2C9A = [62], R5C89 = [21]
3j. R1C9 = 9 (hidden single in R1)
4a. R9C7 = 2 (hidden single in C7) -> R9C6 = 5
4b. R8C7 = 5 (hidden single in R8), placed for NR4C5
4c. 9 in NR4C5 only in R567C6, locked for C6 -> R3C456 = [982]
4d. Naked pair {17} in R4C36 -> R4C45 = [52], R5C4 = 7
5a. R6C2 = 2 (hidden single in R6) -> R1C12 = [28], RBC2 = 3, R3C12 = [31], R8C13 = [83], RBC14 = [48], R4C12 = [64], R5C123 = [964], 4,9 placed for NR4C3, R2C13 = [79], R5C6 = 3
5b. R9C1234 = [1974], R56C5 = [57], R4C36 = [17], R6C34 = [83]
6a. R3C9 = 7 (hidden single in C9) -> R3C8A = [64]
6b. R123CA = 13, R23CA = [24] -> R1CA = 7
and the rest is naked singles.