[Variant "FFA"]
1. i2-i4 .. b9-c9 .. f13-f12 .. Nn10-l9
2. Kh1-i2 .. b10-d10 .. e13-e11 .. Nl9-n10
3. Ki2-j3 .. b6-d6 .. k13-k11 .. m8-k8
4. Nj1-k3 .. Qa7xf2 .. Rk14-k12 .. Bn9-j5
5. Nk3-i2 .. Qf2-g3+ .. Rk12-j12 .. Bj5-d11+++###
[Variant "FFA"]
1. i2-i4 .. b9-c9 .. f13-f12 .. Nn10-l9
2. Kh1-i2 .. b10-d10 .. e13-e11 .. Nl9-n10
3. Ki2-j3 .. b6-d6 .. k13-k11 .. m8-k8
4. Nj1-k3 .. Qa7xf2 .. Rk14-k12 .. Bn9-j5
5. Nk3-i2 .. Qf2-g3+ .. Rk12-j12 .. Bj5-d11+++###
[Variant "FFA"]
1. g2-g4 .. b10-d10 .. i13-i11 .. m6-k6
2. Bf1-j5 .. Ba9xe13 .. Qh14xm9 .. Kn7-m6
3. h2-h3 .. Be13xm5 .. Qm9-i5 .. Km6-l5
4. Qg1xm7 .. b9-c9 .. f13-f12 .. Nn10-l11
5. Bj5-d11+++###
[Variant "FFA"]
1. i2-i4 .. b6-d6 .. e13-e11 .. m8-k8
2. Kh1-i2 .. Qa7xf2 .. Bf14xb10 .. Bn9-j5
3. Ki2-j3 .. Qf2-j6 .. Bb10xj2 .. Nn10-l11
4. Kj3-j4 .. b9-c9 .. f13-f12 .. Bj5-d11+++###
@Martin0 you found the fastest assisted triple checkmate. I found the fastest unassisted on I think.
@e4bc4qh5qf7, not sure why you want to distinguish assisted/unassisted checkmates, The goal was just the quickest, wasn't it? The checkmates happens simultaneous in ffa, so I'm not sure what you think should be patched. Reds king can't really survive by blues king being checkmated and at the same time blues king survive because reds king is checkmated. It creates a contradiction.
[StartFen4 ""]
[Variant "FFA"]
1. g2-g4 .. b9-c9 .. f13-f12 .. m6-k6
2. Qg1-g3 .. b10-d10 .. e13-e11 .. Kn7-m6
3. j2-j3 .. Na5-c6 .. Nj14-i12 .. Km6-l5
4. Bi1xm5 .. Nc6-a5 .. Ni12-j14 .. Kl5-k5
5. Bf1-j5 .. Na5-c6 .. Nj14-i12 .. Kk5-l5
6. Qg3-i5 .. Nc6-a5 .. Ni12-j14 .. Kl5-k5
7. Bj5-d11+++###