These two sentences are both valid
I write this sentence.
I do write this sentence.
Are these both valid?
I am writing this sentence.
I do be writing this sentence.
These two sentences are both valid
I write this sentence.
I do write this sentence.
Are these both valid?
I am writing this sentence.
I do be writing this sentence.
The rule of Do-Support applies to every main verb in English, except auxiliary verbs.
Do-Support is the process that provides the dummy auxiliary do to carry the tense and swap with the subject in Yes/No- and Wh-Questions
tag questions
and negations
However, there are two important qualifications for this rule:
The verb be is always treated as an auxiliary verb, even if it's the only verb in its clause. I.e, it can never invoke Do-Support. Which is the answer to the OP's question.
Other isomorphs of do can occur with be, however:
The verb have, in its sense of "possess", may be treated
"I do be (something, something)....." is used regularly in everyday speech in South-East Ireland, where I grew up, but it is not regarded well, and a sign of being from a very specific type of rural, working class background. Its used in this context as a continuous present: "I do be always listening to that radio show on my way home from work"
What the second of the first pair is doing is adding emphasis. Because we normally use the auxiliary verb "do" in interrogative and negative sentences, not positive sentences.
Question: Do you like apples?
Positive sentence: You like apples.
Negative sentence: You don't like apples.
However, "do" is used in a positive sentence to add emphasis.
Ex.
If my guess is right and you're trying to duplicate the act of emphasizing in the second pair, then it should be done this way:
First pair:
I write this sentence.
I do write this sentence.
Second pair:
I am writing this sentence.
I am writing this sentence.
As you can see, there is no need to add another auxiliary verb in the second pair because the word "be" or "am" is already one.
Do is not usually used as a modal verb. Other answers have explained this and discussed the non-modal use of do with the verb be.
However, do is used as a modal verb to indicate continuous aspect, in some dialects English, as shown in Do be doing be’s: habitual aspect in Irish English.
Thus the strict answer to the question of whether the modal do can be used with the verb be is:
Yes, when do is a modal verb it can be used with the verb be.
All except the last are grammatical, but the second would be found only infrequently. In some regional dialects the construction illustrated by I be writing this sentence is also found.