It really depends on what you call a radical? Hereās an example with four or five āradicalsā (or components, rather), even if some are repeated: ē (ććć). Itās probably not on WK, and itās also probably not very common (in Japanese anyway; I learnt it in Chinese, and I havenāt seen it āin the wildā in Japanese yet), but Iām just raising it for the sake of discussion. Among common, everyday kanji, you might say that ę is a combination of 2å, 1ę„ and 1ę, or simply of é¾ŗand ę. (To be honest, I have no idea what exactly é¾ŗmeans. Apparently it represents the sun in the midst of grass in ę.)
Anywayā¦
While learning Chinese while growing up, and even now, when I encounter new kanji, I look out for components that I already know as kanji (because those usually form bigger blocks). Thereafter, I remember the kanji based on the āsub-kanjiā I recognise. The rest of my āstrategyā tends to involve knowing how to write kanji though, since that helps me remember the position of the components based on their order of appearance in the written form, and I tend to kinda just āmakeā myself remember the reading or the meaning (ideally both) based on something in the kanji, like how it looks.
As an exampleā¦ OK, in order to remember ē« (ćć¾ć©, which shouldnāt be on WK), I remembered that the bottom component is something like āturtleā (äŗ, which used to be é¾ ā I know some of the traditional kanji forms, which helps with stuff like this. Truth is though, the bottom component is actually 黽, which isnāt āturtleā at all), then I noticed the å inside it, which means āearthā. That makes sense because ē« refers to a traditional wood/coal stove made of bricks/earth, or a hearth. I know that the thing at the top is basically a small ē©“: you could say thatās the ācave/holeā radical, which makes sense as well because you need a hole in the wall to put firewood in. Weird stuff like that. I donāt come up with all this consciously. Some components just seem more obvious/sensible, and I use them to help me.
I think the original mnemonic for ę used to contain four components: wolverine + cloth + hand + å (IDK what WK calls it, and I canāt name it in Chinese either). That comes pretty close to five āradicalsā, and is probably an excessive breakdown, even if itās not hugely problematic since the components are relatively simple. I canāt think of any kanji with more than four components that might appear on WK though, aside from 鬱, which youāve already mentioned.
Hereās to hoping that @cringe knows of some in English, because everything Iām aware of is written in Chinese or Japanese. I mean, popular kanji courses outside of WK like āRemembering the Kanjiā, āThe Kodansha Kanji Learnerās Courseā or āEssential Kanjiā generally have at least a bit of etymology in them, but not all of it is accurate or serious, since some of it is just there for the sake of helping people remember. The one resource I do know of is http://www.visualkanji.com. Not sure how good it is though, regardless of the authorās credentials, because I donāt know if sheās an etymology specialist. Another option would be to look at Kayo-sensei (aka @Kayoshodo) on Twitter, because she occasionally posts stuff about kanji origins, in addition to lists of common words and writing tips. Sheās a Japanese calligrapher, but she posts in English. I donāt always agree with whatās said by these sources about etymology, but as Kayo-sensei says, there are multiple theories, and since most of my theories come from Chinese sourcesā¦ well, perhaps some disagreement is to be expected.