How to make CounterIncrement step in increments of 2

This works. Thank you for the help!

SetOptions[InputNotebook[], 
     CounterAssignments -> {{"ItemNumbered", -1}}]

    SetOptions[InputNotebook[], 
     StyleDefinitions -> 
      Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
        Cell[StyleData["ItemNumbered"], 
         CellDingbat -> 
          Cell[TextData[{CounterBox["ItemNumbered"], "."}], 
           FontWeight -> "Bold"], CellMargins -> {{81, 10}, {4, 8}}, 
         StyleKeyMapping -> {"Tab" -> "SubitemNumbered"}, 
         CellFrameLabelMargins -> 4, 
         CellChangeTimes -> {3.657516045744032`*^9},
         CounterIncrements -> {"ItemNumbered", "ItemNumbered"}, 
         CounterAssignments -> {{"SubitemNumbered", 
            0}, {"SubsubitemNumbered", 0}}, MenuSortingValue -> 1630, 
         FontFamily -> "Arial", FontSize -> 15, 
         Global`ReturnCreatesNewCell -> True]}, WindowSize -> {808, 751}, 
       WindowMargins -> {{Automatic, 20}, {16, Automatic}}, 
       FrontEndVersion -> 
        "10.3 for Mac OS X x86 (32-bit, 64-bit Kernel) (October 9, 2015)",
        StyleDefinitions -> "PrivateStylesheetFormatting.nb"]]

SetOptions[EvaluationNotebook[]
, StyleDefinitions -> Notebook @
  { Cell[StyleData[StyleDefinitions -> "Default.nb"]]
  , Cell[StyleData["ItemNumbered"], CounterBoxOptions -> {CounterFunction -> (#*2-1&)}]
  , Cell[StyleData["SubitemNumbered"], CounterBoxOptions -> {CounterFunction -> (#*2-1&)}]
  , Cell[StyleData["SubsubitemNumbered"], CounterBoxOptions -> {CounterFunction -> (#*2-1&)}]
  }
]

As pointed out by @Kuba, the same CounterFunction must be applied to items, sub-items and sub-sub-items to ensure that the counters at all levels match.

Example:

Do[
  If[j === 1 && k === 1, CellPrint@Cell["item", "ItemNumbered"]]
; If[k === 1, CellPrint@Cell["subitem", "SubitemNumbered"]]
; CellPrint@Cell["subsubitem", "SubsubitemNumbered"]
, {i, 3}, {j, 3}, {k, 2}
]