As Alan Munn commented, the desired number of names in citations you describe seem to follow APA rules. If the rest of your style is also APA (or very APA-like), you may want to think about using biblatex-apa
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
\usepackage[style=apa, backend=biber]{biblatex}
\addbibresource{biblatex-examples.bib}
\begin{document}
\cite{nussbaum,sigfridsson,companion,aksin}
\cite{nussbaum,sigfridsson,companion,aksin}
\printbibliography
\end{document}

You can try to emulate a similar cite name scheme by setting maxcitenames=2
and changing the value of the maxnames
counter locally to 6
for the first citation (as tracked by \ifciteseen
and citetracker
). That should work for both biblatex-chicago
and the standard styles.
\documentclass[british]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage{babel}
\usepackage{csquotes}
%\usepackage[style=authoryear, maxcitenames=2, backend=biber, citetracker]{biblatex}
\usepackage[authordate, backend=biber, uniquename=false, mincitenames=1, maxcitenames=2, citetracker]{biblatex-chicago}
\addbibresource{biblatex-examples.bib}
\makeatletter
\AtEveryCitekey{%
\ifciteseen
{}
{\defcounter{maxnames}{6}}%
}
\makeatother
\begin{document}
\cite{nussbaum,sigfridsson,companion,aksin}
\cite{nussbaum,sigfridsson,companion,aksin}
\printbibliography
\end{document}

See also @Audrey's answer to biblatex – et al. beginning from second citation? and @samcarter's answer to How to get et al. beginning with the 2nd citation with biblatex-chicago. biblatex - et. al for specific cases might also be relevant.
That all said, you mention the American Economics Review in the comments and a short google search leads to https://www.aeaweb.org/journals/aer/submissions/accepted-articles/styleguide which suggests
LaTeX authors should refer to either: http://www.aeaweb.org/templates/latex_templates.zip for the LaTeX template (tex). Or, if you wish to have the ability to collaborate with Scientific Word authors, please use: http://www.aeaweb.org/templates/latex_sw-supported.templates.zip Please be sure to include the .aux
file and .bbl
if available.
and later
LaTeX and Scientific Word users, please use the aea.bst
file provided in the template package.
aea.bst
file provided in the template package." So I suggest you ditchbiblatex
in favour of the journal template.