If you want to seriously double and you have not been doing so since before you had any idea of what you are doing...which was my case a a doubler on tenor tbn. and tuba from 3rd grade right up through 4 years of college (

)...you need to understand the differences in the way you play the instruments. And I mean the way you play them.
Physically.
Air. Quantity and how it is focused.
Embouchure as it relates to ranges and different sized rims. (If you are going to use different sized rims, of course. I recommend using m'pces that are at least somewhere near the mainstream for given instrument sizes and idioms; others disagree.)
And you also need a strong, cogent set of "models" on your new horn(s), people who play it the way you want to be able to play it.
And this means...at least it has meant for me since I began to try to understand exactly how I had been doubling on tuba when it began to negatively affect my progress on my main small tenor playing...that you need to begin to understand how you play your main axe. Especially where the rubber meets the road...where the lips meet the m'pce rim.
All competent brass players have little shifts that they use to traverse the 2.5+++ octaves that are pretty much absolutely required to be considered a serious player. Mostly we don't "think" about them or consciously create them...they just happen over the learning period from newbie to serious player. That's good, of course...as long as it works well enough for you to be able to play the way you want to play. However, if you want more, you must figure out what you are doing. I have my way...basically freebuzzing and then finding how to put the freebuzz into the horn in a manner that works well with as little adjustment as possible, then connecting the different ranges and settings that ensue using fairly simple Carmine Caruso approaches. Doug Elliott and other Reinhardt-influenced teachers have other ways to get to what I believe to be pretty much the same place, and other broadly successful teaching styles get there other ways...Song and Wind, Tongue and Blow, the many trumpet approaches, almost all of which seem to have very successful proponents.
Exactly "how" to do this on a practical level? How to do it so that it:
1-Works well enough to use the new double
2-Doesn't blow your regular horn out of the water in the process
and
3-Doesn't take 30 years to learn?
I stopped doubling altogether for a number of years. I found at the time...I was a working NYC freelancer in my early 20s and had "lost my chops" and then regained them over a year-long period of working with Carmine Caruso...that playing tuba suddenly affected (in a negative way) what I was working on in my tenor playing, so I sold the tuba I owned to get rid of the temptation to play it and played only one horn and one m'pce (at a time, anyway) for almost a decade. Then Lee Konitz asked me to join his wonderful Nonet on bass trombone. With some trepidation, I said yes, got a bass trombone and started practicing my butt off on it using Carmine's stuff. It worked. It didn't seem to hurt my tenor playing much and...luckily for me...the parts in Lee's band weren't really very low or very loud. They were in the bass range often, but I didn't have to learn how to honk at the time. Over a period of years, I got more than passable on it and started to work as a recording/performing bass tbn./tenor tbn. doubler. Then some tough young students I had been basically teaching for free showed up at my door with a battered Olds BBb tuba that they had essentially stolen from their high school. I stuck my old m'pce in it and it worked almost immediately. Still no bad effects on my tenor playing. Suddenly I'm a tripler. After a while I bought a really good tuba and started working on that as well.
But...I began to notice some bad effects from the tuba playing. Not overall on a daily basis, but if I had to double tuba and tenor on the same gig, as soon as I played a few minutes of tuba my whole tenor feel started to go away. I could play tenor for an hour and then switch to tuba easily, but 5 minutes of tuba would mess up my upper range.
HMMMmmm...
And that's when I first started to think about what I was doing at the lips. Really. It had never entered my mind. I'd been doing it since grammar school. Duh. I could go on here, but I'll keep it simple because over the years I have found that what was happening with me was not the way it happened with many other good doublers. Different "embouchure types" in the Reinhardtian manner have different needs. For me, the simplest way I can put it is that my "reed"...my lips...got much bigger and thicker when I played tuba and then when I went back to tenor I couldn't stuff the bigger reed into the smaller rim.
Duh squared!!!
Once I understood this mechanism I started to consciously practice with that in mind. Again...for me...using Carmine stuff. Back and forth among my (then) three doubles. Get a balance on one; go to one of the others and get a balance on that, then back to the next horn/m'pce combo. Over and over and over.
It worked.
It worked to the point that I found I could do the same thing with any combination of basically six horns...I could play the right instrument for every job.
Eureka!!!
Been doing it ever since.
So...the important part of all this is:
Understand how your embouchure works. Your embouchure. How it works on your main horn through the ranges that your double may require, then what's different when you play your double. And then...back and forth, back and forth with that knowledge.
Works for me...
S.
P.S. By the way...this works up as well. I haven't really pursued it, but for a couple of months...mostly out of curiosity...I messed w/adding trumpet to my stable. Same same. Thinning out the reed so it works on the smaller rim. Duh.