front end – Is there any way to change the box-formatting behavior thoroughly?


Background

The box-formmating behavior is affected by the downvalues of the symbol MakeBoxes. But the formatting behavior is not exactly MakeBoxes, but seems to be the same to menu command “ConvertTo/StandardForm”. There’s an example for the difference: 159959.

Another key process of evaluations in Mathematica is sending the content of evaluating input cell to evaluators. This can be strongly changed by setting the option CellEvaluationFunction (however, for example, this way can’t handle multi-line cell, see: 29264).

Question

Similarly, is there any way to change the box-formatting behavior more than changing the definition of MakeBoxes?

Related Question

(Not essential for understanding this question. You can skip them if you are not interested.)

  1. Is any way to change the cell-creation behavior which is similar to If(# =!= Null, CellPrint@Cell(BoxData@MakeBoxes@#, "Output"(* , ... *))) &?

  2. Difference between “ConvertTo/InputForm” and MakeExpression(76056), “ConvertTo/StandardForm” and MakeBoxes. (As jkuczm mentioned here, they uses BoxForm`ConvertForm)