I have an existing third floor deck (10'x40'). It is supported by a
6"x12" beam resting on 18' tall 8"x8" posts.

My question: I want to install a second floor deck, underneath the
existing deck, by tying into the existing posts. Which is the best
way? One contractor recommended notching into the existing posts and
inserting 4x12 beams. This seems like more work and also means
cutting halfway into the post and weakening it. Another contractor
said to tie into the post with custom made hardware or maybe a Simpson
connector. This method seems simpler, but will the ties support the
weight of a deck and people?

I haven't seen either method in any of the how-to books. They always
show the beam resting on top of the post.

Thanks,
Karamo