As for me, the most important and highest priority ones:
- Mahoutsukai no Yome season 2 (The first season came out in 2017, but it has been continued in a different format more recently with the three episode OVA beginning its release in 2021, but I want a full-fledged TV-aired second season) (Last season released in 2017). *This series at present and since my introduction to it has sat just outside my Top 20 in ranking, but it's one of the very few which has a high chance to kick the door into the Top 20 and potentially even take its place within the exalted Top 10 depending on its ultimate length, how much further it's fleshed out (length + depth), and which direction is ends up going in, which is pivotal.
- Noragami season 3 (Last season released in 2015)
- The Melancholy of Haruhi Suzumiya season 3 (Last season released in 2009)
- Aku no Hana season 2 (Last season released in 2013)
- Kenpuu Denki Berserk (yes, the 1997 iteration) season 2 (Last season released in 1997)
- Usagi Drop season 2 (Last season released in 2011)
- Kodomo no Jikan season 3 (Last season released in 2009)
- Petshop of Horrors (either season 2 or a reboot of a full-length season/multiple full-length seasons in general, since the first and only season was only a miniscule four episodes) (Last season released in 1999)
- Digimon Tamers - Would have liked to see the full-fledged sequel/follow-up in whatever form before Konaka got "canceled" by the usual Puritan religious-crusasder-esque ideologue mob (Last season released in 2001)
- Centaur no Nayami season 2 (Last season released in 2017)
- Flying Witch season 2 (Last season released in 2016)
- Kemono Friends season 3 (Ideally with season 2 retconned as an abortive flub) (Last season released in 2019)
Also,
- Sora no Woto (Last season released in 2010)
- Hyouka season 2 (Last season released in 2012)
- Hakumei to Mikochi season 2 (Last season released in 2018)
- Gakkougurashi! season 2 (Last season released in 2015)
- Houkago Saikoro Club season 2 (Last season released in 2019)
- Zipang season 2 (Last season released in 2004)
- Somali to Mori no Kamisama (Last season released in 2020)
- Sakurako's Investigation - Beautiful Bones (Last season released in 2015)
- Grimgar of Fantasy and Ash (Last season released in 2016)
Also, a few more very recent series it's far too soon to have more of an accurate prognosis as to whether or not they'll continue in the next few years or not, if ever, but which I would be very receptive and definitely watch a second season for as well, would be a few series from 2021:
- Hataraku Saibou Black (season 2)
- The Idaten Deities Know Only Peace (season 2)
- So I'm a Spider, So What? (season 2)
- Banished from the Hero's Party, I Decided to Live a Quiet Life in the Countryside (season 2)
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