How do you let out a garment that is too tight in the armpits?

As far as Patagonia goes, a pull-over can have a very different cut than a full zip version using the same type of fabric. I had a full zip R1 jacket (like a cardigan really) that was much larger than an R1 Flash pullover, both in XL size.

I would try a Cabela's equivalent. The "hook and bullet" oriented clothing tends to be fuller cut. The military Power Dry tops are fuller cut to the point that they are more like a full size larger.

Pinch out some fabric with your fingers – under the armpit – two layers of fabric, the sleeve and the body – from the outside of fabric

Sew it with a curved seam, and then cut off the excess fabric – maybe 1 inch wide at bottom, curving up to zero on both front and back. 1/4 inch from seam.

Then turn fabric inside out and sew another row of stitches, capturing the raw edge inside so it won't unravel

Look up French Seam on thru-hiker.com articles

Those sounds like instructions to take the item in; OP wants to let it out because it's too tight.

Well beyond my sewing skills, but I assume you will have to add open up the seam under the pit area and add some fabric. Maybe something "netty" for added ventilation?

Add gussets.

http://www.blogforbettersewing.com/2012/01/how-to-sew-two-piece-underarm-gusset.html

Hey Jerry
What you are suggesting just makes it tighter under the armpits!
Gussets or similar are needed. tricky stuff.

Cheers

I've done that before and it made it better.

The problem was the hole in the main fabric was too small, and the bottom edge rubbed against my armpit.

You have to put on your jacket. Pinch off some fabric with your fingers and sort of imagine what would happen if it was cut off a bit.

Be mindful that if you sew and cut you may ruin the jacket

Ah – my misunderstanding. I thought you meant a vertical pinch. My fault.

Reshaping the arm hole would work, but I would not cut anything off the sleeve part, just the body at the bottom edge of the hole. But that does require a bit more skill.

Cheers

If you sew through sleeve and body, it's much easier. I guess we're saying pretty much the same thing : )

I find sewing a sleeve onto a body is about the most difficult sewing task. This avoids that problem.

I would let it out on the Gear Swap. Then use the money to buy one that fits.

or if you bought it from REI, return it

But then you deprive yourself of a project : )

Yeah but…a custom mesh-gusseted or pit-zipped Cap 4 would be the bee's knees, and provide bragging rights for the next decade.

I have some light soft mesh that would be perfect I could send you free

PM me

These people are MYOG enablers, don't listen to them : )

Keeping the Cap 4, sent pm to KC about the mesh, ordered Gütermann Mara tread, and ordered a zigzag attachment for my Singer 221 machine. Now to figure out how to expand those tear-dropped shape gussets.