I believe that under Demolition Delay, you can remodel or change as much as you wish, as long as you don't completely demolish the building. If you did want to demolish the building, then you apply to the Historic & Cultural Landmarks Commission. After the application, you must have a meeting with all interested parties to see if there is a way to save the building, and you have to present your case for demolition to the Commission. After your presentation, they can put a demolition delay on the building up to 180 days. If nothing is done to save your building, then after 180 days, you can demolish it. Under the DD overlay, any remodeling, addition, alterations, repairs, or new construction can occur on the property without being reviewed by the Landmarks Commission.
National Register Designation and being a Recorded Texas Historical Landmark are more ceremonial. You still have to notify the proper authorities that you are going to remodel a building, but they have no legal recourse against you. However, if you are going for Federal or State Tax Credits, or if the project involves public funds, then you do have to adhere to the Secretary of the Interior's Standards for Rehabilitation. If the project is deemed to not adhere to those standards, then the project has to go through a mitigation process. The mitigation process can also be initiated if the project affects federal lands or areas under federal control or regulation. An example of this would be a project that has an impact on the Trinity River. Believe it or not, several preservation projects have resulted from mitigation.