apalike is not one of the 'native' natbib styles. It is much older than natbib and does not support all of natbib's features (for example it does not support the starred commands \citet* and \citep*).
The desired output can be achieved by editing the .bst file.
Locate apalike.bst on your machine. You can do this by typing kpsewhich apalike.bst into the command line/terminal. Alternatively, obtain a copy of the file from CTAN http://mirrors.ctan.org/biblio/bibtex/base/apalike.bst
Copy the file to a location where TeX can find it. The document directory will do fine. See also https://texfaq.org/FAQ-inst-wlcf
Rename the file to apalike-three.bst, say (the license of apalike.bst requires you to change the name if you modify the file)
Find FUNCTION {format.lab.names} (ll. 841-587) and replace the complete function definition with
FUNCTION {format.lab.names}
{ 's :=
s #1 "{vv~}{ll}" format.name$
s num.names$ duplicate$ duplicate$
#3 >
{ pop$ pop$ " et~al." * }
{ #2 <
'pop$
{ #2 =
{ s #2 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
{ " et~al." * }
{ " and " * s #2 "{vv~}{ll}" format.name$ * }
if$ }
{ ", " * s #2 "{vv~}{ll}" format.name$ *
s #3 "{ff }{vv }{ll}{ jj}" format.name$ "others" =
{ " et~al." * }
{ ", and " * s #3 "{vv~}{ll}" format.name$ * }
if$}
if$
}
if$
}
if$
}
Find FUNCTION {calc.label} (ll. 896-912) and replace the complete function definition with
FUNCTION {calc.label}
{ type$ "book" =
type$ "inbook" =
or
'author.editor.key.label
{ type$ "proceedings" =
'editor.key.label % apalike ignores organization
'author.key.label % for labeling and sorting
if$
}
if$
"(" % these three lines are
* % for apalike, which
year field.or.null purify$ #-1 #4 substring$ % uses all four digits
*
")" *
'label :=
}
This change is necessary to avoid natbib misparsing the name list.
Add a comment with your name, the current date and a short description of the changes to the top of the file.
Use \bibliographystyle{apalike-three} instead of \bibliographystyle{apalike} in your document.
As alternative for steps 1 to 5 you can obtain the patched version of the file at https://gist.github.com/moewew/e3d3ed6ebc93b5e05d6394813f5ad3e5
Then
\documentclass{article}
\usepackage{natbib}
\bibliographystyle{apalike-three}
\begin{filecontents}{\jobname.bib}
@article{asdf3,
title = {asdf},
author = {One, One and Two, Two and Three, Three},
journal = {asdf},
volume = {1},
number = {1},
pages = {1--2},
year = {1234},
}
@article{asdf2,
title = {asdf},
author = {One, One and Two, Two},
journal = {asdf},
volume = {1},
number = {1},
pages = {1--2},
year = {1234},
}
@article{asdf1,
title = {asdf},
author = {One, One},
journal = {asdf},
volume = {1},
number = {1},
pages = {1--2},
year = {1234},
}
@article{asdf4,
title = {asdf},
author = {One, One and Two, Two and Three, Three and Four, Four},
journal = {asdf},
volume = {1},
number = {1},
pages = {1--2},
year = {1234},
}
\end{filecontents}
\begin{document}
\citet{asdf1}
\citet{asdf2}
\citet{asdf3}
\citet{asdf4}
\bibliography{\jobname}
\end{document}
gives

apalikeandnatbibyou're not usingbiblatex. If you're making this many changes (as in your previous question) you may want to switch tobiblatexsince it's generally easier to modify (no.bstfiles). I would recommendext-authoryearstyle as a beginning (not thebiblatexapa, style which is not designed to be modified since it implements the exact APA style). – Alan Munn Aug 21 '20 at 22:34biblatexseems to be a bit costly—is this kind ofapalike-natbibcombination deprecated? – Junyong Kim Aug 21 '20 at 22:58makebstto generate your own.bstfile instead. – Alan Munn Aug 21 '20 at 22:59apaliketoo? I am checkingbiblatexnow, but it seems quite different from what I am using. – Junyong Kim Aug 21 '20 at 23:25