Toppling kings in multipartite tournaments by introducing new kings

Let t=(t1,t2,…,tn) and c=(c1,c2,…,cn) be two nn-tuples of nonnegative integers. An all-4-kings nn-partite tournament T(V1,V2,…Vn)T(V1,V2,…Vn) is said to have a (t,c)-property   if there exists an nn-partite tournament T1(W1,W2,…,Wn)T1(W1,W2,…,Wn) such that for each i∈{1,…,n}i∈{1,…,n}: (1)Vi⊆WiVi⊆Wi;(2)exactly titi 4-kings of ViVi are not 4-kings in T1T1;(3)exactly cici 4-kings of WiWi are not vertices of ViVi. We describe all pairs (t,c) such that there exists an nn-partite tournament having (t,c)-property.