grammatical ponderings

In my notation a simple grammatical structure is represented as a triple of the form [subject | action | object] with elements of the triple annotated with gliphs to represent tense, belief etc.

One of the elements that has never satisfied me is constructions that are kind of three way sentences such as “john threw the ball to tom”
which in the notation is represented as [john | throw_p | <to, tom, ball>] It could of course be written as two statements

[john | throw_p | ball]
[ = tom]

But this is a little long winded, so what I need is to be able to consisely represent such a common sentence structure using N.

Any ideas? How about [john | throw_p | [ = tom]]
still makes me think that we don’t break up the meaning of the sentence in that way when we use the three way construction, so what is going on in our heads? Is there a third party along with the subject and object?