What is the purpose of 是 in "我应该是感冒了"?
I do not agree that 是 is acting as the copula in the sentence. Because even without 是, the following sentences contain the same meaning and only differ in tone:

我应该是感冒了
我应该感冒了

This answer comes after reading
「是」，「的」與動詞名物化 by professor 石定栩 of PolyU in Hong Kong. (The title roughly translate to: 是, 的, and Normalization of Verb)
感冒 should be acting as a verb in the sentence, as 是 can be optionally added to the sentence to add stress to the statement. 我应该是感冒了 conveys the meaning of: &quot;I think I am really having a cold.&quot;
TL;DR, Professor Shi proposes that &quot;是&quot; used in a sentence like

他這樣做是合情合理的。 (What he did was very reasonable) VS
他這樣做合情合理。 (What he did was reasonable)

should be treated as a modal verb, before the main verb of the sentence &quot;合情合理&quot;, with &quot;是&quot; treated as a modal verb the same way the 2 other referenced papers have had it analyzed.
By the same argument, I believe we can treat 感冒 as the main verb, and 是 as a modal verb, used to intensify the tone of the sentence.
By removing all descriptive words, the sentence simplifies into: &quot;我感冒了&quot;, which still carries the essential meaning.

P.S. I believe some Chinese linguists actually prefer treating 应该 and 是 as just verbs (with 是 pointed out in the paper referenced), which would have changed the sentence analysis. However, for some people, it may be more acceptable to allow for modal verbs in Chinese grammar analysis, with the above argument.