It's not clear whether the series will develop into an S3, 或者 a series of OVAs yet.
Pro S3: the 预览 for EP25 showed some indication that Azunyan was going to make good on her promise to keep the keion-bu alive, which means she needs at least three 更多 members to 加入 (just as Yui made the 4th member to make HTT in S1). Therefore another interesting development is 更多 members are going to be added to the story, I'm hoping one of Azunyan's 'mob' (the classmates, most likely Jun) we already got a glimpse of in S2.
Anti S3: There are very few (if any, I can think of perhaps one) 日本动漫 that 显示 HS graduates integrate into college life. But that isn't written in stone, either -- K-ON is known for exceptions to the rule. How many female 日本动漫 songs have topped Oricon? (^- ^ )
The 日本漫画 stopped at S2... but that means little.
OVAs are atractive to 日本动漫 houses, because they're much, much 更多 profitable than an 日本动漫 series, even one as monstrous as the K-ON franchise. They have the luxury of being produced in chunks, so interruptions of funding are less likely to result in substandard quality. They have 更多 desirable special features and bundled accessories 你 won't get on TV, and profit is immediate.
I'm hoping for an S3... but I'm in the camp where all stories must end, and if 你 do have to go, go with class... and EP24 说 without a doubt, 'Oshimai' -- 'The End'. If EP25 and EP 26 are simply an epilogue for what happens to Azunyan and HTT afterwards, I'm cool with it. The series is awesome for its classiness and warmth, and one-off stories can always live on, on BD.