I have never negotiated or know anyone who has negotiated with Landmark commission. I know doubt that you might be in for a long fight, i have never seen this accomplished, but not saying this impossible. If you are in a historic Neighborhood what gave you the initial idea that it was possible, are there others in the area that you have seen that have done this. If the answer is no, then your chances are getting slimmer. Being a TIC is a hurdle also how many people will be involved and this could make it more complicated.
Talk to some contractors, get bids and ask them if it is possible. A local contractor that is in the area will usually know the history of the additions and remodels and could probably tell you a story or too about how hard it was to accomplish certain permits.