Anything is possible. It's just a question of how much you're willing to spend.

About how much a sq ft?

About how many square feet are involved?

Are you prepared to:

--Have a professional design an appropriate new roof;

--Obtain a building permit;

--Remove and store all furnishings and decorative items;

--Protect flooring;

--Remove all existing roofing, gutters and downspouts;

--Remove all roof and ceiling framing, sheathing and insulation;

--Remove all HVAC, electrical and signal formerly above the ceiling;

--Replace everything with new stuff;

--Cleanup;

--Install furnishings and decorative items

Oh...and not live in or use that portion of your house for 6 months (If everything goes well).

Anything is possible and sometimes expensive; impossible things are even more expensive.

...And take even longer .

The original, front, section of your house has a hip roof. It would take considerable time and money to have the entire original roof removed and replaced with a gable roof.

A much more practical approach -- which would have considerable positive effect on the curb appeal -- would be to remove only that forward facing slope on the right side (in front) and create a forward facing gable on that section of the roof from left of the door to the right front corner of the home. Once that existing forward downward slope is removed, you could then create a forward facing gable to replace it using the same slope as the side ridges of the hip roof that was removed. You could have your forward facing gable cover only what the forward slope had covered OR, better yet, continue that ridge line and forward facing gable to cover and additional front porch -- six or eight feet deep.

The addition sticking up over the original part of the house is the visual culprit here. It is going to continue sticking up in back until you add a second floor to the front part. Given the money involved on any of the suggested solutions, I would forget a fix and just keep it as-is. My first house was a cute little one-story on a nice corner. The folks who bought it from me added a monster two-story addition in back, which wasn't pretty from any angle but looked especially awful from the side street. The house was eventually demolished and replaced by a completely new house.

Is this house in FL? If it is, you don't want to switch to a gable roof unless you're willing to pay for extra strapping, etc.

@cpartist...we're in Los angeles. And @Virgil Carter Fine Art of course we are prepared for all of that. We already remodeled the entire kitchen, took walls out, remodeled 2 bathrooms, all new flooring, etc. But thank you for the list.

So the time to have done this was when you did the interior redo not now unless of course you have money to burn and want to do the redo again. Someone already messed up this house I do not think messing it up more will help.

I'd start the redesign process by going for a contemporary look. To do this I'd remove the front segment roofs and extend the rear roof all the way forward. Add different siding/trim and a contemp door. A wrapping porch may fit. You could have high side windows for interior light. You'll need a talented architect with a portfolio of contemporary designs.

The changes you mentioned can be done if you are willing to pay. You said you have already been through a "remodel". This isn't a remodel. This is a build job. If your roof goes higher then so do your walls. The front of your house will almost be rebuilt from the floor up to the new roof. This is a very expensive change. But can certainly be done!!

Sure, a couple of hundred thousand spent on rebuilding the house again can cure the problem you created with a bad addition design. But you might want to pause and get an architect involved to be sure that there aren’t unintended consequences of that rebuild as well.

hire brick and batten to do a few mock ups - they do some amazing work https://www.brickandbatten.com/exterior-design-services/

The lower section walls might be extended and a new roof added with cathedral ceilings but the problem will be how to extend the walls and maintain their structural integrity and how to determine the structural capacity of the existing foundation.

Tell us the type of foundation and what the walls are made of. Are there any construction drawings at the local building department?