LaTeX

\def\@footnotemark{...\@makefnmark...}
\long\def\@footnotetext#1{...\@makefntext{#1}...}

with the index suplied to both places in \@thefnmark. We set the following hooks.

\def\@footnotemark{...\a:@makefnmark\@makefnmark
                                           \b:@makefnmark...}
\long\def\@footnotetext#1{...\a:@makefntext
                \@makefntext{\b:@makefntext
                                   \a:@makefnbody #1\b:@makefnbody
                            }\c:@makefntext...}

<..latex ltfloat ..>+
\pend:def\@footnotemark{\bgroup
   \expandafter\ifx \csname @makefnmark\endcsname\relax \else
     \pend:def\@makefnmark{\hbox\bgroup\a:footnotemark}%
     \append:def\@makefnmark{\b:footnotemark\egroup}%
   \fi
}
\append:def\@footnotemark{\egroup}
\NewConfigure{footnotemark}{2}
\NewConfigure{footnotebody}{2}
-_-_-

<..latex ltfloat ..>+
\long\def\@footnotetext#1{\leavevmode
    \vbox{%\IgnorePar
       \leftskip0pt {\ht:everypar{}\parindent0pt\leavevmode}%
       <.makefntext for footnotetext .>%
       \reset@font\footnotesize
       \color@begingroup
         \@makefntext{\ignorespaces#1}%
       \color@endgroup
       \ht:special{t4ht@[}}\ht:special{t4ht@]}}
\NewConfigure{footnotetext}{3}
-_-_-

<..makefntext for footnotetext ..>
\long\def\:tempc##1{<.footnote label .>\a:footnotetext
\o:@makefntext:{\b:footnotetext \csname a:footnotebody\endcsname
{##1}\csname b:footnotebody\endcsname}\c:footnotetext
}%
\HLet\@makefntext\:tempc
-_-_-

<..footnote label ..>
\protected@edef
\@currentlabel{\csname p@footnote\endcsname\@thefnmark}%
\anc:lbl f{footnote}%
-_-_-

The following arises in cases like ‘ \begin{minipage}{6in} x\footnote{The} \end{minipage}’.

<..latex ltfloat ..>+
\long\def\@mpfootnotetext#1{\leavevmode
    \vbox{%
       \leftskip0pt {\ht:everypar{}\parindent0pt\leavevmode}%
       <.makefntext for mpfootnotetext .>%
       \reset@font\footnotesize
       \color@begingroup
          \@makefntext{\ignorespaces #1}%
       \color@endgroup
       \ht:special{t4ht@[}}\ht:special{t4ht@]}}
-_-_-

<..makefntext for mpfootnotetext ..>
\def\:tempc##1{<.mpfootnote label .>\a:footnotetext
\o:@makefntext:{\b:footnotetext \csname a:footnotebody\endcsname
{##1}\csname b:footnotebody\endcsname}\c:footnotetext
}%
\HLet\@makefntext\:tempc
-_-_-

<..mpfootnote label ..>
\protected@edef
\@currentlabel{\csname p@mpfootnote\endcsname\@thefnmark}%
\anc:lbl f{footnote}%
-_-_-

<..latex ltfloat ..>+
\def\FNnum{\the\c@footnote}
\def\:tempc{%
    \HAssign\FNnum = \csname c@\@mpfn\endcsname
    \HAdvance\FNnum by 1
    \o:footnote:
}
\HLet\footnote=\:tempc
\def\:tempc[#1]{%
    \HAssign\FNnum = #1\relax
    \o:@xfootnote:[#1]%
}
\HLet\@xfootnote\:tempc
\def\:tempc{%
    \HAssign\FNnum = \c@footnote
    \HAdvance\FNnum by 1
    \o:footnotemark:
}
\HLet\footnotemark\:tempc
\def\:tempc[#1]{%
    \HAssign\FNnum =  #1\relax
    \o:@xfootnotemark:[#1]%
}
\HLet\@xfootnotemark\:tempc
\def\:tempc{%
    \HAssign\FNnum = \csname c@\@mpfn\endcsname
    \o:footnotetext:
}
\HLet\footnotetext\:tempc
\def\:tempc[#1]{%
    \HAssign\FNnum = #1\relax
    \o:@xfootnotenext:[#1]%
}
\HLet\@xfootnotenext\:tempc
-_-_-