Force ibid in citation when using non-standard page numbers

Question

I am using BibLaTeX, and I need to cite a source by its headings, not by its page numbers. Is there any way to force BibLaTeX to use ibid when the title and location are the same?

Note: questions Biblatex: tricks with repeated citations in footnotes and Ibid for citations with same title and page do not address this issue. I specifically need to cite using something other than the simple page number.

As far as I can see, I have used the correct package options (e.g., ibidpage=true). Here is the minimum working example:

\documentclass{book}

\usepackage
    [backend=biber,
     style=verbose-ibid,
     citepages=omit,
     ibidpage=true,
     firstinits=true]
   {biblatex}

\usepackage{filecontents}

\begin{filecontents}{ibid.bib}

@book{a,
  title    = {Summa theologiae},
  author   = {{Thomas Aquinas}},
}

\end{filecontents}

\addbibresource{ibid.bib}

\begin{document}

Here is some reference.\footcite[2]{a}
Here is some reference.\footcite[2]{a}
Here is some reference.\footcite[I, q.~1, a.~4]{a}
Here is some reference.\footcite[I, q.~1, a.~4]{a}
\printbibliography

\end{document}

The footnotes I get for the first two, which use a standard page number are

¹ Thomas Aquinas. Summa theologiae, p. 2.
² Ibid.

as expected. However, the other two, which uses the headings, produces

³ Ibid., I, q. 1, a. 4.
⁴ Ibid., I, q. 1, a. 4.

The desired output for the fourth footnote is simply

⁴ Ibid.

Can this be done?

Answer 1

The ibidpage option in verbose-ibid sets loccittracker=constrict implicitly (see verbose-ibid.cbx). loccittracker=strict will not only distinguish footnote and body citations and suppress potentially ambiguous situations, it will also "check[...] if the postnote argument is numerical (based on \ifnumerals [...])." (pp. 60 sq. of the biblatex documentation).

That means that

Here is some reference.\footcite[2]{cicero}
Here is some reference.\footcite[2]{cicero}

is recognised as the same postnote because it is the same postnote in both cases and the postnote is numeric. But

Here is some reference.\footcite[I, q.~1, a.~4]{cicero}
Here is some reference.\footcite[I, q.~1, a.~4]{cicero}

does not pass the test even though the two postnotes are identical because they are not numeric as tested by \ifnumerals.

We can override this behaviour explicitly with loccittracker=context. With that option biblatex does not consider the outcome of the \ifnumerals test when checking for matching postnotes.

\documentclass{book}
\usepackage[backend=biber, style=verbose-ibid, citepages=omit,
  ibidpage=true, firstinits=true, loccittracker=context]{biblatex}
\addbibresource{biblatex-examples.bib}

\begin{document}
Here is some reference.\footcite[2]{cicero}
Here is some reference.\footcite[2]{cicero}
Here is some reference.\footcite[I, q.~1, a.~4]{cicero}
Here is some reference.\footcite[I, q.~1, a.~4]{cicero}
\end{document}