Here are the top 30ish non-jouyou, non-jinmei kanji from several frequency databases. I compiled these a while ago for my own curiosity and don't readily have references to the source data (other than the excel file I made).
The kanji in each list (except for the last one) are in descending order of frequency with the most frequent first.
Aozora Bunko
學處爺體當厭妾叩顏覗會對聲嘘歸掻發鼠儘變呆數噛慾狐關經睨呟
Newspaper
嶽渕澤涌槿舛趙尹鉾靱妓聯諫潘舘銚筧苫炳粕桓橿荊姦薮扮捏頸鮫禱
Twitter
嘘艸垢澤奢餃糞卍叩彡琲罒噛呟騙咳舐罠芒炒灬贅苫遽煽乁洒覗痒揉
Wikipedia
澤學牝魏牌鐵曰欅祀叩渕濱讐癌趙輌舘嘘苫狗吊譚站讀綬廠姦薇憑罠
Top 50 Jinmei from Newspaper
伊晋幌之也鵬菅彦阿弘圭智浩龍笠菱旭桐宏嶋柏李祐昌萩函遼嘉敦筑吾栗尖輔奄亮佑幡篠峯淳翔俣蔭稀堺磐毅乃哉
(EDIT: These were completely incorrect before the edit. I skipped part of the data when copying.)
These are the ones that appear in more than one list (so they are probably the most useful)
澤嘘姦罠覗叩呟噛學渕舘苫趙