Just to add some further thoughts: it would be great if this third font had a large family and many weights – as it would probably become the main font for the supplement and I'd like a lot of variation, but that may be too much to ask for.

I don't think you should add a third font to the mix, unless it's very compatible in style to one of the two existing ones. It sounds like a better idea to replace Etica entirely, if you're sure you no longer like it.

What about this?
https://monokrom.no/fonts/telefon

hhp

What Hrant said. Maybe, for added flexibility you could look for something with both sans and slab designs (like many of Type Together offerings, for example).

Thanks for the replies.

I was afraid you would say that – and deep down, I think you're right. How about if I was to only use two combinations at a time? Which I suppose is not what I was looking for, but it's a start. Unfortunately, I don't think I could suddenly swap out LFT Etica ... from the broadsheet, anyway.

For instance, I just spotted this from Type Together's "Type in Use" section.

They use Coranto 2 and LFT Etica in the main section, and Bree and Adelle in the other section. I'd like a font with some more flair to use with Coranto 2 in the newspaper's supplements, and I wouldn't use LFT Etica in them then. But I'd like it to feel like it was in the same "extended family", if you know what I mean. I don't think Telefon is the right fit, although I do love it.

A bold slab could be useful.
I went bold in two directions with Pratt Nova, both high contrast and slab, which gave the Globe designers lots of options.
http://webmedia.newseum.org/newseum-multimedia/dfp/pdf4/CAN_TGAM.pdf

I will be releasing that later in the year.
In the meantime, I would say look for a somewhat condensed slab face, especially one with some thin weights that would be useful at large display size in the supplements. Perhaps you might also persuade TT to do an ultra-fine version of Coranto for that kind of usage.

Thanks Nick – that's really helpful. Pratt Nova is absolutely stunning. Was it custom for the Globe?

Would you also be of the opinion that adding a third typeface to the main mix is a bad idea? I would never use it in a way that would allow it to compete with the other two fonts. For instance, The Observer in the UK has a mix of three going on, but they seem to complement each other very well:

Somehow, I actually think this could be fine.

And that is a slab, too.

Thanks for the kind words, Edmund.
Yes, Pratt was custom for the Globe.
I originally published it commercially in 2009, but in a subsequent redesign we made substantial changes and additions (hence the “Nova” apellation), which I have not yet updated in the commercial release.

Yes, I do think that a third style can complement a sans+serif main combo, and a slab can do the trick.
But these days, I see no reason not to use something more exotic, a rounded style or a script for instance, perhaps distressed.

Of course, the key is to provide sufficient contrast in style (caps – lower case – italic), size, weight and even colour, between the typefaces.

Nick, those words were more honest than "kind" – the typography in the Globe really makes me envious.

I think you give some fantastic advice there: I am searching for good rounded and slab matches. Any suggestions would be appreciated. I think a script would be a bit too much for me to take, although I agree the consideration has some merit.

The most important bit is the sufficient contrast – that really is key.

Reading your earlier post above again, I was surprised your mention of an "ultra fine" Coranto commission didn't bring our own custom work to my mind. While it may not be ultra fine, we did a lighter version in house of Coranto for some of our section heads:

I am sure though you may not be impressed with some of the aspects like the kerning and our quick-turnaround custom job (it was done in a few days just before we launched our redesign), because I haven't been back to fix some of the problems that irk me since, but it has served us well.

Once again, thanks everyone for your help!

Beware, many foundries don’t allow modifications of their fonts. From TypeTogether’s EULA:

you are not permitted to alter the Font Software in any way, such as by decompiling, reverse engineering, disassem- bling, modification, or altering or changing the Font Software or any associated embedding bits or convert the Font Soft- ware for use as a webfont without prior written notice to and the express permission of TypeTogether.

Don't worry – we have not altered the font software. The section heads are actually just modified outlines in Illustrator.