In the lyric of イノコリ先生, there is a phrase that surprised me. It goes like : 手を上げられないです。does this mean です can come after verb? such as 来られるです. What if the verb is polite? Should you add です or not? 来られます。来られますです(?). What is the difference between 来られるです and 来られます? Does it is restricted only for potential form verbs?
The short answer:
You can think of です as performing several funcitons. Being a polite form of the copula だ, or being an auxiliary polite helper verb.
です as a politeness helper verb:
- No you cannot say 来られるです. The polite present form of the verb is 来られます.
You can only append です as a politeness helper for い-adjectives, so 来ないです is fine because ～ない is syntactically a い-adjective.
When it is not a polite helper, you only see です when it is needed to express past tense in 来られませんでした. Politeness is already accounted for by the helper verb ます. In the present tense you do not say 来られますです.
The long answer is to look at the conjugation rules of verbs and of い-adjectives.
You may be slightly confused with the い-adjective conjugation scheme, which can use です as its politeness helper highlighted in yellow below:
As a result you see that there are two negative polite forms. So for example you can have 暑くないです・暑くありません and their past forms 暑くなかったです・暑くありませんでした where we note that でした accounts for past tense and ません has already accounted for politeness in 暑くありませんでした.
Now to complete the earlier table for verbs, we note that ない is syntactically a い-adjective and obeys the conjugation rules for い-adjectives. So now for verbs we have:
This is why you see 上げられないです, but you cannot get 来られますです or 来られるです.
To add です after a verb is incorrect. You must use ます after them. So 来られるです and 来るです are incorrect. 来られます is natural and れる,られる means not only "potential" but also "respect", "passive", and "spontaneous".
And if you change a verb to a honorific word, the verb become polite. For example, いらっしやる is a honorific word of 来る.
In addition, ない in 手を上げられないです isn't a verb but a verbal auxiliary which means negative. Some verbal auxiliaries before です doesn't grammatically seem to be correct in a precise sense but they are commonly used. And you can rephrase it as 手を上げられません。