Can "be" be used with the modal verb "do"?

Solution 1:

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

• Do you still love her?
• What do you love about her?

tag questions

• You still love her, don't you?

and negations

• You don't love her any more.

However, there are two important qualifications for this rule:

1. 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:

   • Do be a "Doo Bee", and don't be a "Dont Bee". - Emphatic do, active noun predicates.
   • What I'm gonna do is be her bodyguard. - Active do, active noun predicate.

2. The verb have, in its sense of "possess", may be treated

   • either as an auxiliary verb, i.e, commuting with the subject: Have you the time?
     (marked as "British" in American English)
   • or as a main verb, i.e, allowing Do-Support:
     Do you have the time? (by far the more common choice in N. America)

Solution 2:

"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"