Here are the three symbols you mention:

\documentclass{article}
\usepackage{amsmath}
\DeclareRobustCommand{\frommnsymbol}[3]{%
%1 = atom type, #2 = mnsymbol font, #3 = character
#1{\text{\usefont{U}{MnSymbol#2}{m}{n}\symbol{#3}}}%
}
%\DeclareFontFamily{U}{MnSymbolA}{}
%\DeclareFontFamily{U}{MnSymbolB}{}
%\DeclareFontFamily{U}{MnSymbolC}{}
\DeclareFontFamily{U}{MnSymbolD}{}
%\DeclareFontFamily{U}{MnSymbolF}{}
%\DeclareFontShape{U}{MnSymbolA}{m}{n}{
% <-6> MnSymbolA5
% <6-7> MnSymbolA6
% <7-8> MnSymbolA7
% <8-9> MnSymbolA8
% <9-10> MnSymbolA9
% <10-12> MnSymbolA10
% <12-> MnSymbolA12}{}
%\DeclareFontShape{U}{MnSymbolB}{m}{n}{
% <-6> MnSymbolB5
% <6-7> MnSymbolB6
% <7-8> MnSymbolB7
% <8-9> MnSymbolB8
% <9-10> MnSymbolB9
% <10-12> MnSymbolB10
% <12-> MnSymbolB12}{}
%\DeclareFontShape{U}{MnSymbolC}{m}{n}{
% <-6> MnSymbolC5
% <6-7> MnSymbolC6
% <7-8> MnSymbolC7
% <8-9> MnSymbolC8
% <9-10> MnSymbolC9
% <10-12> MnSymbolC10
% <12-> MnSymbolC12}{}
\DeclareFontShape{U}{MnSymbolD}{m}{n}{
<-6> MnSymbolD5
<6-7> MnSymbolD6
<7-8> MnSymbolD7
<8-9> MnSymbolD8
<9-10> MnSymbolD9
<10-12> MnSymbolD10
<12-> MnSymbolD12}{}
%\DeclareFontShape{U}{MnSymbolF}{m}{n}{
% <-6> MnSymbolF5
% <6-7> MnSymbolF6
% <7-8> MnSymbolF7
% <8-9> MnSymbolF8
% <9-10> MnSymbolF9
% <10-12> MnSymbolF10
% <12-> MnSymbolF12}{}
\newcommand{\ntriplesim}{\frommnsymbol{\mathrel}{D}{"7E}}
\newcommand{\nlessgtr}{\frommnsymbol{\mathrel}{D}{"C0}}
\newcommand{\ngtreqlessslant}{\frommnsymbol{\mathrel}{D}{"C7}}
\begin{document}
$a\ntriplesim b$ $a\nlessgtr b$ $a\ngtreqlessslant b$
$X_{a\ntriplesim b}$ $X_{a\nlessgtr b}$ $X_{a\ngtreqlessslant b}$
\end{document}
I commented out the unused fonts.
The font declarations are directly borrowed from MnSymbol.sty. How are the letter and code determined?
I looked in MnSymbol.sty for the three symbols
\Decl@Mn@Char\ntriplesim {MnSyD}{\mathrel}
\Decl@Mn@Char\nlessgtr {MnSyD}{\mathrel}
\Decl@Mn@Char\ngtreqlessslant {MnSyD}{\mathrel}
This determines the letter to use. Unfortunately, MnSymbol doesn't use explicit codes for the symbols, but there's a trick for getting them without counting in the file: latexdef -p MnSymbol followed by the symbols' names will show the necessary codes.
> latexdef -p MnSymbol ntriplesim nlessgtr ngtreqlessslant
\ntriplesim:
\mathchar"377E
\the\ntriplesim:
14206
\nlessgtr:
\mathchar"37C0
\the\nlessgtr:
14272
\ngtreqlessslant:
\mathchar"37C7
\the\ngtreqlessslant:
14279
Thus I can supply as character code the last two digit in the \mathchar representation.
MnSymboldoes not provide.fdfiles, but defines all the information usually found in.fdfiles instead in the.styfile. it should not be difficult to extract that into.fdfiles, using as a model the method used formathabx. but that certainly wouldn't avoid "wasting a precious math alphabet resource". – barbara beeton Dec 23 '18 at 02:51