How can I create a list with a step size different from 1?

You can create a new command that does the trick with everything you know about counters ;)

\documentclass{article}

\newcommand{\myitem}{\addtocounter{enumi}{3}\item}

\begin{document}
\begin{enumerate}
  \myitem One
  \myitem Two
  \myitem \dots
\end{enumerate}
\end{document}

You could create a new command with a step size as argument as well:

\newcommand{\myitem}[1]{\addtocounter{enumi}{\numexpr#1-1\relax}\item}

Or "set a step size" in the beginning:

\documentclass{article}

\let\olditem\item
\newcommand{\myitem}[1]{\addtocounter{enumi}{\numexpr#1-1\relax}\olditem}
\newcommand{\setenumstep}[1]{%
  \renewcommand{\item}{\myitem#1}
}

\begin{document}
\begin{enumerate}
  \myitem4 One
  \myitem4 Two
  \myitem4 \dots
\end{enumerate}

\begin{enumerate}
  \setenumstep{4}
  \item One
  \item Two
  \item \dots
\end{enumerate}
\end{document}

These enumerations both result in the same as the first one posted.

Probably you know it already, but might be helpful anyway: If you want to tweak single items, you can do it manually with

\item[4.] One
\item[8.] Two

If you're not concerned about \labeling the \items, you can use the following setup:

\documentclass{article}

\usepackage{enumitem,etoolbox,xfp}

\newlist{fourenumerate}{enumerate}{4}
\setlist[fourenumerate]{label = {\mulfour{\value*}.}}

\newrobustcmd{\mulfour}[1]{\inteval{#1 * 4}}

\begin{document}

\begin{enumerate}
  \item One
  \item Two
  \item \ldots
\end{enumerate}

\begin{fourenumerate}
  \item One
  \item Two
  \item \ldots
\end{fourenumerate}

\end{document}