Syntax: How can this tree be built?

Question

I am working through "Contemporary Linguistics" on my own. It's been going pretty well, but I have a question about building syntax trees.

I understand the tree here for "The dog might bite that man" fairly well. Now, I would like to add "tomorrow" to the end of the sentence. I've looked through the book, and the only similar example I can find is using "never", which comes in front of the verb.

Is this there a Move happening here?

Tomorrow the dog might bite that man.

This is correct grammar, but I don't see anything to attach tomorrow to on the left side of the sentence.

*The dog might tomorrow bite that man.

This is not correct grammar, and I believe that means tomorrow could not have moved from there?

I don't quite know if "The dog tomorrow might bite that man" is correct grammar, but it seems much less ungrammatical than *"tomorrow bite". Could the adverb attach to the I?

How can I build this tree?

Answer 1

Tomorrow simply becomes a part of a Verbal Phrase (VP):

update 2

I'
. I: might
. VP
. . VP
. . . V: bite
. . . NP
. . . . DET: that
. . . . N: man
. . PP
. . . Adv: tomorrow

Also, note that there are two possible formal representations:

1. bite tomorrow, as pictured above;
2. might tomorrow, when tomorrow becomes a part of epistemic modality verb phrase (I' in your diagram);

I guess the clash may be caused by mixing language-specific and language-agnostic semantic graphs.
The former are often vulnerable to artifacts that prevent displaying them into a nice tree-style structure. Maybe the simplest example would be separable prefixes in German language:

Ich fange mit der Arbeit an ("I begin with studying")

Here, VP is mit der Arbeit, but the V itself splits into two words around its VP, which can't be represented with a nice tree. In a language-agnostic semantic graph, there is no such problem.