Pretty much every brake offers a reach adjustment, but free-stroke adjustment is something else entirely. You'll see it on some high-end models, but even those might not go far enough for riders who like these crucial touch points to be extra touchy. If you're even slightly comfortable bleeding brakes, you can hack your own reach adjustment.
If you pull your brakes without your wheel installed, the pads will compress but won't completely retract. You can use this to your advantage. Remove your wheel, and carefully pull the brake lever about halfway in. Reinstall the wheel, and check if your brake feels any tighter. If not, repeat the process but pull the lever very slightly further and check your work again. Unfortunately, this is especially difficult on four-piston brakes because the pistons will almost never come out uniformly, so I only recommend doing this with two-piston models. Once you've found the feel you want, you'll have to add fluid. What you've just done is forced fluid from the lever reservoir into the system pushing your pads in and essentially "tightening" your brake. But you'll have to replace that fluid that came out of the reservoir or else it will eventually go back. Luckily, you only have to address this at the lever. Exactly how depends on the brake you have. In this video, it is a SRAM Level, which is designed to be bled with a syringe at the lever. Nearly any brake with a threaded bleed port at the lever can be done this way. Fill your syringe with the proper type of oil and remove all bubbles. Remove the bleed port plug and attach the syringe. The bladder inside the brake lever will expand because you've pushed some of its contents into the system, so you've created bubbles. Pulling on the syringe will compress the bladder and pull the bubbles out. You'll need to do it a couple times until the bubbles stop appearing. Push on the syringe to make sure there is no suction in the lever, remove the hose, and replace the bleed plug.
Other brakes will work differently. Shimanos use a plastic cup at the lever, and you can simply attach a full cup to the bleed port, pull the lever, and it will fill the reservoir. Other brake levers allow you to expose the reservoir, and it's as simple as opening it up and filling it with fluid.
Once you've got a proper bleed, you'll need to re-adjust your caliper. This is crucial because you now have a lower margin of error, so you will have to work hard to keep it from rubbing. Once you sort that out, you will have successfully hacked your free-stroke adjustment.