BEFORE:
Our grammar will not generate sequences like:
Hagrid arranged for Harry to buy his books in London

Words like for and to, at present, are analyzed as prepositions that combine with NPs to make PPs. However, the sequences:
for Harry to buy his books in London
to buy his books in London
...appear to have prepositions followed by sequences of words that are not NPs.

AFTER:
Our current class grammar has phrase rules that allow the prepositions "for" and "to" to head PPs with NP complements, like in (1).

(1) Sean is going back to Rhode Island for winter break.

However, certain instances of "for" and "to" cannot be generated by the grammar, like in (2).

(2) We arranged for Sean to go back home.

Our phrase structure rules cannot generate (2) because the element following "to," "go back home," is not an NP, as the PP phrase structure rule requires.

Additionally, the word "for" is followed by an NP, "Sean," so it may seem that the PP phrase structure rule can generate a PP "for Sean." However, looking at the constituency of (2)...

What did we arrange? *For Sean. For Sean to go back home.

..."for Sean" is not a constituent, so to use a phrase structure rule to model "for Sean" as a PP would be incorrect.

Since sentences like (2) exhibit "for" and "to" followed by elements that the phrase structure rules cannot generate after them, we will need new phrase structure rules that generate other types of phrases after "for" and "to."

[ Can I immediately conclude that a new phrase structure rule is needed? ]