Why do you want to increase your range? How you answer this will help someone who may wish to answer your question. There is nothing you cannot accomplish given honest hard work and patience while you progress.
In my opinion, one must have a solid musical reason for increasing their range. Not saying you are like this, but just wanting to impress, "Betty Sue, the cheerleader" or wanting to be the highest player at Camp "Higher, Faster, Louder," this summer are not good enough reasons. Hear me out... Why would I say this?
Because any reason outside of yourself is ultimately a fickle one and will fail you. When you decide just what it is you want to do with your higher range, your creative mental activity will kick into high gear and you will begin eating up all the good advice any of us throws at you. Until then, you will mired in the quicksand of, "closed throat, open throat, breath support, too much pressure, Stevens embouchure, etc." Not a good place to be, believe me!
My good friend, free your mind, set a musical goal, play purely, play intentionally, enjoy. Now for my advice. I'm doing this myself now and I'm no beginner. Get yourself the Getchell Book of Practical Studies, book 2 and begin on the first page, playing each etude up an octave, slowly and softly and BEAUTIFULLY! When you make it through the first one, go on to the next one playing slowly, softly and BEAUTIFULLY. If you do not enjoy making music in that register, no amount of arpeggios, Stamp, Maggio, etc., is going to ultimately make any difference- though you will benefit from applied practice of those methods, too.
Study this sentence: "The aesthetic qualities of an insight are closely bound to its validity."
Here's what I think it means. You go for the gold! In trumpet playing that is: a beautiful sound and exquisite personal style. As you play the melodies in the upper register, and love what you are doing presently and enjoy the level you are on, the range will increase as you continue the hard work. And if what you are doing does not sound beautiful- you are wrong. Kick back a notch and begin again. Beauty is an unquestioned aspect of music- despite what our friends the tastee bros may assert.
No secrets, Mike. Like Nike, "Just Do it!"