Occidental
About a hundred years ago, Esperanto was making waves all over Europe for being an IAL that wasn't complete torture to study. Volapuk had kind of fizzled out because it was an awful language, its name alone remaining as some form of mockery in various natural languages and Esperanto. Also, its creator was being kind of an ass.
However, Esperanto was by no means perfect. In fact, there was a whole lot wrong with it, so everybody and their dog decided they could do better. The most blatant of these attempts was a language called Ido, which is the Esperanto and Ido suffix for "offspring." It started from Esperanto as a base and made improvements to its flaws while unwittingly introducing new ones. Besides Ido, there was also Giuseppe Peano's Latino Sine Flexione which, true to its name, was less a newly created language and more Latin reforged into a language without inflections, as well as Otto Jespersen's Novial ("new IAL"), which criticized Esperanto's Eurocentrism without being able to fully escape it itself. I've read Jespersen's publications about Novial, and it's actually quite a competent language, if not for screwing everyone outside of Europe over.
But this page isn't about Ido, LSF, or Novial. This page is about another language that attempted to be the arithmetic mean of the Romance languages: Occidental. Despite being extremely Romance, Occidental was designed by someone outside that sphere. And yet perhaps precisely because of that (and the fact that he had been a Volapukist, then an Esperantist, then a frequent correspondent of Peano and Jespersen, among others), the Estonian Edgar de Wahl was able to create the most elegant nu-Latin of all, striking a sublime balance between naturalism and schematicness. And yes, I say that even knowing how much of its vocabulary is Germanic.
Anyone who's studied Latin knows that its verbs have more or less two distinct themes: the present theme and the perfect theme, like how the present active infinitive for "to write" is "scribere," but its perfect active infinitive, "to have written," is "scripsisse," which further leads to forms like the supine "scriptum." Latin has no surefire way to derive a verb's perfect theme from its present theme; it's just one more thing you get to memorize about every single verb you learn. This matters because it's the perfect theme that so often gets used in derived words from which Romance languages draw a lot of shared vocabulary.
But de Wahl was clever. When designing Occidental, and obviously basing the bulk of its verbs off of Latin, he devised a simple rule for forming their perfect stems. In the majority of cases, this made them look close enough to their Latin perfect stems to be aesthetically pleasing to Romance speakers, and in cases where the stems differed too much, he simply made the Occidental present stems closer to the Latin perfect ones in the first place. This "de Wahl's Rule," as it's called, is so elegant that there's less than ten verbs in the entire language that it can't save. Considering the task he was attempting, a single-digit number of irregular verbs, and only in one form at that, is damn impressive, and his rule would even be lifted for use in Dr. Olivier Simon's Sambahsa. Modern Occidentalist Leo Stief has even developed "Stief's Rule," which gets verbs even closer to their Latin perfect stems at the cost of several more irregulars.
In designing prefixes and suffixes for use with these stems (and other parts of speech) in word formation, de Wahl sought less to ascribe meaning to them from on high and more to extract some sort of regularity and schematicness from the affixes already visible in Romance languages. Since there's only so much regularity actually there, he only succeeded to a limited extent. There's like four or five suffixes for turning an adjective into a noun, and I have no idea what the difference between them is supposed to be. However, there's no denying that Occidental's affixes are very productive, and it's eminently possible to form words like "successosi" (successous?) that no Romance language has made, but potentially could've. The takeaway is that to use Occidental's affix system effectively, you mostly just have to go with your gut... which is only really going to be possible for speakers of languages that already have similar-looking affixes, i.e. the Romance languages and English, making it a piss-poor IAL. For this reason, its modern community doesn't really approach it as an IAL in the first place.
Yes, that's right: it still has a community, albeit a small one. It was one of the many twentieth-century modern Latin wannabe IALs to fall into decline, but unlike your LSFs and Mondials, Occidental has been raised from the dead. Quite impressive, considering what it's been through. In 1951, the International Auxiliary Language Association developed a language called Interlingua that looked a whole lot like Occidental minus a distressing amount of regularity. Rather than fight this competitor, Occidentalists sought to join hands with them, even changing the name of their own language to "Interlingue" to reflect the languages' similar natures when they caught wind of Interlingua's development. Though Stalin's persecution of an unrelated group of extremists called the "Occidentalists" probably played a part in the name change, too. Unfortunately for Occidental's speakers, the IALA wasn't terribly interested in them, and Interlingua would go on to grow and develop independently, maintaining to this day a niche following of mostly Romance-language speakers that can easily handle the language's irregularities. Occidental was left for dead.
But recent years have seen a revival of interest in Occidental thanks to the efforts of one man: Dave MacLeod, a programmer (I think?) who lives in South Korea and also goes by Mithradates or Dhghomon on the internet. What exactly did he do, you ask? Oh, he just created the single best piece of pedagogical material ever written for any IAL, that's all.
Dhghomon's "Salute, Jonathan!" is a very long graded reader that teaches you Occidental in Occidental from absolutely nothing, progressing until you're just straight-up reading literature. That's no exaggeration, either, because SJ is actually a translation and adaptation of a piece of classical literature that you have certainly heard of. Make no mistake: SJ is the reason I took enough interest in Occidental to see its appeal and make this page. The advent of the internet did see a slight resurgence for Occidental due to the simple fact of people having a convenient forum to learn and discuss the language, but the way I see it, SJ is what made it explode. Relatively speaking, of course.
Couple Dhghomon's masterwork with the resurfacing of several publications from the heyday of auxlanging (apparently Occidentalists and Idoists liked to get in pissing matches), and suddenly there was plenty of content to enjoy in this language. Nowadays, everyone interested in this curious little gem from a century ago congregates in the Occidental Discord server and has a grand old time shooting the shit. If you want to know more, take a gander at Occidental-lang.com. It has literally everything you could ever want for the language, including a link to SJ.