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you can flatten then MapThread
{{{a,b,c}, {e,f,g}}, {{h,i,j}, {k,l,m}}} // Flatten[#,1]& // MapThread[Plus,#]&MapThread[Plus]
(* {a + e + h + k, b + f + i + l, c + g + j + m} *)
{{{a,b,c}, {e,f,g}}, {{h,i,j}, {k,l,m}}} // Flatten[#,1]& // MapThread[Plus,#]&
{{{a,b,c}, {e,f,g}}, {{h,i,j}, {k,l,m}}} // Flatten[#,1]& // MapThread[Plus]
