How to make the “〜でも” form of normal verbs and i-adjectives?

Question

There's something that irks me. The particle “〜でも” can be inserted after many parts of speech such as:

駅にでも行った？

In this sense it occupies much the same grammatical place as “〜は” or “〜も" in that it follows other particles but replaces “〜が” an “〜を”. We can however mark verb-like parts of speech with them and say:

1. 行きはする
2. 到着はする
3. 綺麗ではある
4. 犬ではある
5. 美しくはある

But with “〜でも” this is not the case. I remember at one point I wanted to ask something like “寝でもした？”. It felt awkward to me when I asked it and native speakers later confirmed to me that it didn't feel quite right either. However I do feel that we can say:

1. 到着でもする
2. 綺麗ででもある
3. 犬ででもある

With suru-verbs, na-adjectives, and nouns.

Though admittedly the last two also feel a little bit shaky to me, perhaps due to the double “で” but not nearly as much as:

1. 行きでもする
2. 美しくでもある

So is it simply not possible to mark verbs and i-adjectives with “〜でも”? Because to me the nuance it would impart in “寝でもした？” feels like a natural choice in the context of asking someone whether that person went to be already similar to “Did you actually go to be already or something?” and seemingly with suru verbs it's fine to say “抗議でもする気？” for “Do you feel like actually protesting or something?”. I also don't feel that with suru-verbs it promotes the verb to an actual object as in “日本語の勉強をする” opposed to “日本語を勉強する” after all. We can say “日本語を勉強でもする” which shows that “勉強” must still be part of the verb and cannot be the actual object. Similar to how we can say “これを見はする”.

Answer 1

Unfortunately, not everything can be neatly explained by simply applying the basic rules of grammar, and this may be one of such cases. It's true that でも is classified as a 副助詞, and it's natural to expect it to behave like this chart. However, that may not be the case here.

• 行きでもしたら, 寝でもすると and so on are not incorrect to me. However, for verbs, there happens to be a suitable word, たり, which is normally preferred. I also vaguely feel the shortness of 寝る might have something to do with the acceptability of 寝でもする, but I'm not sure. Of course, 抗議でもする気か, 昼寝でもしよう and so on are always perfectly fine since they are suru-verbs.
• 美しくでもある is clearly wrong. It's hard for me to even imagine what it's supposed to mean. Again, we can use たり to add a sense of "or something" here. What you may be trying to say can probably be expressed like "美しかったり(する?)".