How do I make future equations renumber as extensions of previous equations?

Question

I'm looking to do the following automatically rather than manually

\documentclass{article}
\usepackage{amsmath}

\begin{document}
These equations are pretty important.

    \begin{align}
        \label{eqn:one}     a+b&=c\\
        \label{eqn:two}     d+e&=f\\
        \label{eqn:three}   g+h&=i
    \end{align}

But as it turns out, we can actually do better by recalling
    that $a=1$, so we have

    \begin{equation*}
        \tag{\ref{eqn:one}A}
            1+b=c\\
    \end{equation*}

Furthermore, $c=d=e=2$, so we have

    \begin{align*}
        \tag{\ref{eqn:one}B}    1+b&=2\\
        \tag{\ref{eqn:two}A}    2+2&=f
    \end{align*}

\end{document}

In other words, I'd like to provide a switch that tells an equation to display a number based on which iteration of a previous equation it is. Non-requirements:

• I can manually instruct it which equation is its ancestor; I don't need it to "figure it out" automatically.
• I also don't care what the format of these numbers is as I presume any solution will make that easy to change (so e.g. I'd be just as happy with 1.1, 1.2 instead of 1A, 1B).
• Finally, there is no need to support automatic re-labeling, as I can manually re-label the important future iterations so long as the label "grabs" the tagged-displayed number in references.

Requirement:

• The one thing that is essential is that I would like to automate the sub-numbering process so I don't risk messing it up by moving equations around / deleting them.

Unfortunately I'm not sure what this is called. Sub-referencing equations? Self-referencing equation numbering?

Answer 1

\documentclass{article}
\usepackage{amsmath}

\def\subeqncount#1{%
\newcounter{sub:#1}%
\expandafter\def\csname thesub:#1\endcsname{\ref{#1}\Alph{sub:#1}}}

\def\subeqntag#1{%
\refstepcounter{sub:#1}%
\tag{\csname thesub:#1\endcsname}}


\subeqncount{eqn:one}
\subeqncount{eqn:two}

\begin{document}
These equations are pretty important.

    \begin{align}
        \label{eqn:one}     a+b&=c\\
        \label{eqn:two}     d+e&=f\\
        \label{eqn:three}   g+h&=i
    \end{align}

But as it turns out, we can actually do better by recalling
    that $a=1$, so we have

    \begin{equation*}
           \subeqntag{eqn:one}
            1+b=c\\
    \end{equation*}

Furthermore, $c=d=e=2$, so we have

    \begin{align*}
        \subeqntag{eqn:one}    1+b&=2\\
        \subeqntag{eqn:two}    2+2&=f
    \end{align*}

\end{document}