What is the most elegant way to cite two things connected by a 'joining word' with biblatex?

One solution is to use a multicite approach and redefine the \multicitedelim appropriately following “And” between last and second last cite using the \footcites command and authoryear-icomp.

\newcommand{\interp}[1]{%
  \renewcommand*{\multicitedelim}{%
    \ifnumequal{\value{multicitecount}}{\value{multicitetotal}}
      {\addcomma\space\printtext{#1}}
      {}%
    \space}%
  \renewcommand*{\textcitedelim}{%
    \ifnumequal{\value{multicitecount}}{\value{multicitetotal}}
      {\addspace\printtext{#1}}
      {}%
    \space}%
}

We then simply define new multicitecommands

\DeclareMultiCiteCommand{\citeint}[\interp{interpreting}]{\cite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citesla}[\interp{slagging off}]{\cite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citepint}[\interp{interpreting}\mkbibparens]{\parencite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citepsla}[\interp{slagging off}\mkbibparens]{\parencite}{\setunit{\multicitedelim}}
\makeatletter
\DeclareMultiCiteCommand{\citetint}[\interp{interpreting}\cbx@textcites@init\cbx@textcites]{\textcite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citetsla}[\interp{slagging off}\cbx@textcites@init\cbx@textcites]{\textcite}{\setunit{\multicitedelim}}
\makeatother

Which we can then use as

\citeint{ctan}{gillies} and \citesla{ctan}{gillies}

---

You can also use your initial idea of \parencites{ctan}[interpreting][]{gillies}

if you issue a

\AtNextCite{\renewcommand{\multicitedelim}{\addcomma\space}}

before the citation command.

As in

\AtNextCite{\renewcommand{\multicitedelim}{\addcomma\space}}
\parencites{ctan}[interpreting][]{gillies}

---

MWE

\documentclass{article}
\usepackage[citestyle=authoryear-comp,bibstyle=authoryear,backend=biber]{biblatex}
\addbibresource{biblatex-examples.bib}

\newcommand{\interp}[1]{%
  \renewcommand*{\multicitedelim}{%
    \ifnumequal{\value{multicitecount}}{\value{multicitetotal}}
      {\addcomma\space\printtext{#1}}
      {}%
    \space}%
  \renewcommand*{\textcitedelim}{%
    \ifnumequal{\value{multicitecount}}{\value{multicitetotal}}
      {\addspace\printtext{#1}}
      {}%
    \space}%
}

\DeclareMultiCiteCommand{\citeint}[\interp{interpreting}]{\cite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citesla}[\interp{slagging off}]{\cite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citepint}[\interp{interpreting}\mkbibparens]{\parencite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citepsla}[\interp{slagging off}\mkbibparens]{\parencite}{\setunit{\multicitedelim}}
\makeatletter
\DeclareMultiCiteCommand{\citetint}[\interp{interpreting}\cbx@textcites@init\cbx@textcites]{\textcite}{\setunit{\multicitedelim}}
\DeclareMultiCiteCommand{\citetsla}[\interp{slagging off}\cbx@textcites@init\cbx@textcites]{\textcite}{\setunit{\multicitedelim}}
\makeatother

\begin{document}
  Desired output is (CTAN 2006, interpreting Gillies 1933).

  \autocites{ctan}{gillies}

  \citepint{ctan}{gillies} and \citepsla{ctan}{gillies}

  \citetint{ctan}{gillies} and \citetsla{ctan}{gillies}

  \citeint{ctan}{gillies} and \citesla{ctan}{gillies}

  \autocites{ctan}{gillies}
\end{document}

EDIT

Or... er... this gets me the same output as shown below with the same document content:

\newbibmacro*{connectcites:multipostnote}{%
  \setunit{\addcomma\space}%
  \iffieldundef{multipostnote}
    {\printtext{quoting}}
    {\printfield{multipostnote}\clearfield{multipostnote}}%
    \space}
\DeclareMultiCiteCommand{\pconnectcites}[\mkbibparens]{\parencite}{\usebibmacro{connectcites:multipostnote}}

But it probably violates the Biblatex Bible in a hundred different ways....

MWE:

\documentclass{article}
\usepackage[citestyle=authoryear-comp,bibstyle=authoryear,backend=biber]{biblatex}
\addbibresource{biblatex-examples.bib}

\newbibmacro*{connectcites:multipostnote}{%
  \setunit{\addcomma\space}%
  \iffieldundef{multipostnote}
    {\printtext{quoting}}
    {\printfield{multipostnote}\clearfield{multipostnote}}%
    \space}
\DeclareMultiCiteCommand{\pconnectcites}[\mkbibparens]{\parencite}{\usebibmacro{connectcites:multipostnote}}


\begin{document}

  \pconnectcites(interpreting){ctan}{gillies}

  \pconnectcites[see][56]{ctan}[details from][47--89]{gillies}

  \pconnectcites(interpreting)[based on][87]{ctan}[original argument in][32]{gillies}

  \pconnectcites(interpreting)[98]{ctan}[67]{gillies}

  \pconnectcites(interpreting)[see][]{ctan}[an earlier version in][]{gillies}

\end{document}

Original Answer

At moewe's request, I'm posting this as an 'answer' although I don't really consider it one since it is so very far from elegant!

Using penguinpreferred's suggestion and xparse, I come up with this:

\NewDocumentCommand \pconnectcites { D() {quoting} o o m o o m }{%
  \parentext{%
    \IfNoValueTF{#3}{%
      \IfNoValueTF{#2}{%
        \cite{#4}%
      }{%
        \cite[#2]{#4}%
      }%
    }{%
      \cite[#2][#3]{#4}%
    }%
    , #1 %
    \IfNoValueTF{#6}{%
      \IfNoValueTF{#5}{%
        \cite{#7}%
      }{%
        \cite[#5]{#7}%
      }%
    }{%
      \cite[#5][#6]{#7}%
    }%
  }%
}

which allows me to say:

  \pconnectcites(interpreting){ctan}{gillies}

  \pconnectcites[see][56]{ctan}[details from][47--89]{gillies}

  \pconnectcites(interpreting)[based on][87]{ctan}[original argument in][32]{gillies}

  \pconnectcites(interpreting)[98]{ctan}[67]{gillies}

  \pconnectcites(interpreting)[see][]{ctan}[an earlier version in][]{gillies}

to produce: