Multi-lingual / multi-script typefaces

As someone who works daily with books that involve as many as four or five scripts (and their weights and italics and small caps, where applicable), I can tell you that using fonts in which multiple scripts have been loaded can create more problems than they solve, and take more time than when the fonts are individual. This is especially true when one of the scripts is right-to-left and another is left-to-right.

A very long glyph palette can be clumsy and tiring to use, and switching text direction and keyboard layout is more time consuming than switching fonts. This is especially true when the scripts are combined within single paragraphs. 

If the work at hand is typesetting, say, food contents labels, working with a clumsy overloaded font is a chore you can live with, but with more extensive work, such as a book, it can be a curse. Having a Latin set along with another script is often a necessity, but you needn't use it as your primary Latin. In a structured document, in which good use is made of paragraph and character style sheets, switching fonts is no problem at all, and keeping the fonts separate makes editing much easier and faster.

Moreover, I find that most makers of multi-script fonts make decisions regarding relative character height based on ignorance or convenience (e.g., hinting zones), not on what more knowledgeable people might consider best typographic practices, and so the purported advantage of equal weights by size (which is not always desirable) becomes a false one in the end.

Paul, there are quite a few good fonts that can handle your entire list of Latin languages, and even some that include all the Cyrillic variants and the Greek. That would limit your shopping to the last three scripts on your list, or even just two.