In all probability, Ulrike’s answer is what you really want. However, in order to do literally what your question asks for, that is, to force a page break between two paragraphs of a footnote (for example, because you don’t want the footnote to take up so much vertical space on that particular page), you should simply write
\vspace{\maxdimen}
between the two paragraphs in question. The two methods (Ulrike’s and this one) can also be combined:
% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly
% declare the paper format.
\usepackage[T1]{fontenc} % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.
\usepackage{lipsum}
\begin{document}
Blah blah.\footnote{\interlinepenalty = 10000
\lipsum[1-2]
\vspace{\maxdimen}
\lipsum[3-4]
}
\end{document}
Note that replacing
\vspace{\maxdimen}
with
\pagebreak[4]
is not guaranteed to work in every situation, not even if you use
\par \penalty -1000000000
in lieu of \pagebreak[4]
. The reason is explained on p. 123 of The TeXbook: whenever Step 3 applies, Step 4 is not even tried.
More generally, you could force a page break after a certain line in a footnote by placing
\vadjust{\vskip\maxdimen}
somewhere on that line; this will overcome any other setting that might be in force. For example:
% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly
% declare the paper format.
\usepackage[T1]{fontenc} % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.
\usepackage{lipsum}
\begin{document}
Blah blah.\footnote{\interlinepenalty = 10000 \clubpenalty = 10000
\lipsum[1-2]
I~want this footnote to be broken across pages right after the line that
contains \emph{this}\vadjust{\vskip\maxdimen} word. \lipsum*[3]
\lipsum[4]
}
\end{document}
Finally, it should be noted that, if the problem is that you want to limit the vertical space on a page devoted to footnotes, you can do so by setting the value of a length that can be named as \dimen\footins
. For example,
% My standard header for TeX.SX answers:
\documentclass[a4paper]{article} % To avoid confusion, let us explicitly
% declare the paper format.
\usepackage[T1]{fontenc} % Not always necessary, but recommended.
% End of standard header. What follows pertains to the problem at hand.
\usepackage{lipsum}
\begin{document}
\setlength{\dimen\footins}{200pt}
Blah blah.\footnote{\lipsum[1-4]}
\end{document}