Here are some irregular adverbs that defy the rules set up in this post.
- diū, diūtius, diūtissimē, for a long time, for a longer time, for the longest time
- potius, —— potissimum, rather, first of all
- saepe, saepius,saepissimē, often, more often/again, most often
- satis, satius, —— enough, preferable
- secus, sētius, —— otherwise, worse
- multum (or multō), magis (or mage), maximē, much, more, most
- parum, minus, minimē, not enough, less, least
- nūper, ——, nūperrimē, newly, most newly
- temperē, temperius, —— seasonably, more seasonably
Most of these are either disconnected from their corresponding adjectives (semantically), or are defective in either comparative or superlative form. However, the real outlier here is the multum/ō, magis/e, maximē set, which is an aggregate of various options. Multō is of course the ablative singular neuter for the positive adjective, and mage the neuter accusative of the comparative adjective.
Magis and maximē may also be paired with other adjectives to create their comparatives, especially in adjectives ending in -eus or -ius (in the positive.)
- idōneus, magis idōneus, maximē idōneus, fit, more fit, most fit
The Essential AG: 128, 218a
Latin for Addicts 
“secus, sētius”, a good one to note. There’s also a nice adverbial expression with sētius- “nihilō sētius” meaning “nevertheless”.
Someone needs to throw together a book or a webpage of Latin expressions that Latinists can use so as to differentiate ourselves from all the college graduates who μέγα φρονοῦσιν when they use things like ‘ad hominem’ and ‘ipso post facto’ in conversation.