I was solving the Rosetta problem Peaceful chess queen armies just now. The idea is to place q armies of queens, each m large, on a n-by-n chess board such that one army of queen can not capture any other queen. The task there ask us to place 2 armies of each 4 queens on a 5*5 board:

ClearAll[ValidSpots, VisibleByQueen, SolveQueen, GetSolution]
VisualizeState[state_] := Module[{q, cells, colors,},
  colors = DeleteCases[Union[Flatten@state[[All, All, "q"]]], -1];
  colors = Thread[colors -> (ColorData[106] /@ Range[Length[colors]])];
  q = MapIndexed[
    If[#["q"] == -1, {}, 
      Text[Style[#["q"], 20, #["q"] /. colors], #2]] &, state, {2}];
  cells = 
   MapIndexed[{If[OddQ[Total[#2]], FaceForm[], 
       FaceForm[GrayLevel[0.8]]], EdgeForm[Black], 
      Rectangle[#2 - 0.5, #2 + 0.5]} &, state, {2}];
  Graphics[{cells, q}, ImageSize -> Length[First@state] 30]
  ]
ValidSpots[state_, tp_Integer] := Module[{vals},
  vals = 
   Catenate@
    MapIndexed[
     If[#1["q"] == -1 \[And] DeleteCases[#1["v"], tp] == {}, #2, 
       Missing[]] &, state, {2}];
  DeleteMissing[vals]
  ]
VisibleByQueen[{i_, j_}, {a_, b_}] := 
 i == a \[Or] j == b \[Or] i + j == a + b \[Or] i - j == a - b
PlaceQueen[state_, pos : {i_Integer, j_Integer}, tp_Integer] := 
 Module[{vals, out},
  out = state;
  out[[i, j]] = Association[out[[i, j]], "q" -> tp];
  out = MapIndexed[
    If[VisibleByQueen[{i, j}, #2], <|#1, 
       "v" -> Append[#1["v"], tp]|>, #1] &, out, {2}];
  out
  ]
SolveQueen[state_, toplace_List] := 
 Module[{len = Length[toplace], next, valid, newstate},
  If[len == 0,
   tmp = state;
   Print[VisualizeState@state];
   Abort[];
   ,
   next = First[toplace];
   valid = ValidSpots[state, next];
   Do[
    newstate = PlaceQueen[state, v, next];
    SolveQueen[newstate, Rest[toplace]]
    ,
    {v, valid}
    ]
   ]
  ]
GetSolution[n_Integer?Positive, m_Integer?Positive, numcol_ : 2] := 
 Module[{state, tp},
  state = ConstantArray[<|"q" -> -1, "v" -> {}|>, {n, n}];
  tp = Flatten[Transpose[ConstantArray[#, m] & /@ Range[numcol]]];
  SolveQueen[state, tp]
  ]
GetSolution[5, 4, 2]

Notice that no queen of army 1 can capture any queen of army 2 (and vice versa).

But we can go much beyond that, let;s check what can happen for a given chess board size how many we can place for the case of 2 armies:

GetSolution[3, 1]
GetSolution[4, 2]
GetSolution[5, 4]
GetSolution[6, 5]
GetSolution[7, 7]

We can also look at more than 2 armies, let's look at 3 armies:

There are many more things to explore: not only square chessboard but also rectangular chessboard, more colors, other chess pieces…