By "..._MAX" I assume that you mean the maximum value of a given integer type.
In a language where half-open intervals are supported consistently in all the places, this would be solved trivially, e.g. for a signed byte the _MIN and the _MAX values would be defined as -128 and +128, more intuitively than when using closed intervals, where you must remember to subtract 1 from the negated minimum value.
Even the C language has some support for half-open intervals, because the index pointing after the last element of an array is a valid index value, not an out-of-range value (though obviously, attempting to access the array through that index value would be trapped as an out-of-range access, if that is enabled).
Applied consistently, the same method would ensure that the value immediately above the last representable value of an integer type is valid in ranges of that type, even if it would be invalid in an expression as an operand of that type.
In a language where half-open intervals are supported consistently in all the places, this would be solved trivially, e.g. for a signed byte the _MIN and the _MAX values would be defined as -128 and +128, more intuitively than when using closed intervals, where you must remember to subtract 1 from the negated minimum value.
Even the C language has some support for half-open intervals, because the index pointing after the last element of an array is a valid index value, not an out-of-range value (though obviously, attempting to access the array through that index value would be trapped as an out-of-range access, if that is enabled).
Applied consistently, the same method would ensure that the value immediately above the last representable value of an integer type is valid in ranges of that type, even if it would be invalid in an expression as an operand of that type.