I'll post my own answer as I found a pretty simple way to achieve the resut I was looking for.
With the command \DeclareMathAlphabet, which syntax is
\DeclareMathAlphabet{<math-alph>}{<encoding>}{<family>}{<series>}{<shape>}
you can define <math-alph> to be a new math alphabet.
The arguments <encoding>, <family>, <series>, <shape> are the default
values for this math alphabet in all math versions; these can be reset
later for a particular math version by a \SetMathAlphabet command. If
is empty then the is declared to be invalid in all
versions, unless it is set by a later \SetMathAlphabet command.
Checks that <math-alph> can be used and that <encoding> is a valid
encoding scheme.
In these examples, \foo is defined everywhere but \baz, by default, is
defined nowhere.
\DeclareMathAlphabet{\foo}{OT1}{cmtt}{m}{n}
\DeclareMathAlphabet{\baz}{OT1}{}{}{}
(from Index of /ctan-doc/macros/latex/doc/html/fntguide)
All the combination available with the mathalfa package are available in the source code of mathalfa.sty on GitHub. Another list, with all the font abbreviation can be found on the mathalfa documentation (at the end of the pdf).
I found particularly illuminating the answer to this question provided by the user cfr, which I thank for the illustration of the use of command
\DeclareMathAlphabet.
I'll provide a simple example for future visitors:
%PREAMBLE
\DeclareMathAlphabet\mathzapf{T1}{pzc}{mb}{it}
\DeclareMathAlphabet{\mathchorus}{OT1}{cmtt}{m}{n}
\DeclareMathAlphabet\mathrsfso{U}{rsfso}{m}{n}
% ...
%DOCUMENT
\[
\mathzapf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\]
\[
\mathchorus{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\]
\[
\mathrsfso{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\]
which output is

\mathcal,\mathscr,\mathfrak,\mathbb? – GiuTeX Aug 05 '17 at 13:46