Here is a variant of subequations that allows for stepping the parent equation counter.
\documentclass{article}
\usepackage{amsmath}
\usepackage{etoolbox}
\AtBeginDocument{\let\standardtheequation\theequation}
\newenvironment{subequations*}
{%
\subequations
\counterwithin*{equation}{parentequation}%
\let\theequation\standardtheequation
\patchcmd{\theequation}{equation}{parentequation}{}{}%
\apptocmd{\theequation}{\alph{equation}}{}{}%
\newcommand{\substep}{\stepcounter{parentequation}}%
}
{\endsubequations}
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed
do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\begin{subequations*}
\begin{align}
f_1(x) &= x^2 \\
f_2(x) &= x^2 \\
\substep
g_1(x) &= x^2 \\
g_2(x) &= x^2
\end{align}
\end{subequations*}
Lorem ipsum dolor sit amet, consectetur adipiscing elit,
sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\end{document}

With some twisting you can also refer to the global numbers. The label for the \substep number is input as an optional argument to \substep.
\documentclass{article}
\usepackage{amsmath}
\usepackage{etoolbox}
\AtBeginDocument{\let\standardtheequation\theequation}
\makeatletter
\newenvironment{subequations*}
{%
\subequations
\counterwithin*{equation}{parentequation}%
\let\theequation\standardtheequation
\patchcmd{\theequation}{equation}{parentequation}{}{}%
\apptocmd{\theequation}{\alph{equation}}{}{}%
\let\theparentequation\standartheequation
\newcommand{\substep}[1][]{%
\refstepcounter{parentequation}%
\if\relax\detokenize{##1}\relax\else
\ltx@label{##1}%
\fi
}%
}
{\endsubequations}
\makeatother
\begin{document}
Lorem ipsum dolor sit amet, consectetur adipiscing elit, sed
do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\begin{subequations*}\label{first}
\begin{align}
f_1(x) &= x^2 \label{first-a} \\
f_2(x) &= x^2 \label{first-b} \\
\substep[second]
g_1(x) &= x^2 \label{second-a} \\
g_2(x) &= x^2 \label{second-b}
\end{align}
\end{subequations*}
Lorem ipsum dolor sit amet, consectetur adipiscing elit,
sed do eiusmod tempor incididunt ut labore et dolore magna aliqua.
\ref{first} \ref{first-a} \ref{first-b}
\ref{second} \ref{second-a} \ref{second-b}
\end{document}

\refto just (2) without letters? – andywiecko Jan 10 '19 at 12:35