I added 7 inches to my teak platform. I bought a platform that someone replaced (for $75), took all the teak strips apart, then added them to the "boat side" of the platform, one at a time, clamping glueing, and srewing them in place with the screws from the platform I took apart.
It came out good and now we can stand on the platform without feeling like we have to hold on.
To extend the brackets, I bought stainless angle iron from McMAster, and simply bolted them to the top of the existing brackets.
Not the best picture, but all the strips against the transom are the ones I added.