According to page 47 of the HVL-F43AM user manual, the HVL-F43AM can be used as either a WL controller or as an off-camera flash, so yes, if you purchase another HVL-F43AM, you'll be able to remotely control it by using the one you have on the hotshoe of your camera.

However, keep in mind, that unlike the newer "RM" units, the version of the Sony WL system the HVL-F43AM uses is the optical (light-signal) version, not the radio version. It will, however, let you have TTL, HSS, and remote power control over the off-camera flashes.

Also, several third-party flashes (e.g., Godox TT685-S, Metz 44 AF-1, Sigma EF 610-DG, Phottix Mitros+ for Sony, etc.) can use optical WL as off-camera flashes, so you don't have to get a Sony OEM flash.

But optical slaving relies on "line-of-sight", where the sensor on the flash has to be able to "see" the light signals from the controller unit, and is best used where the ambient light is not particularly bright (e.g., in studio conditions). Once you go on location into bright sunlight, most optical wireless systems will lose range and reliability, and have much more stringent line-of-sight requirements (due to the lack of bounce surfaces nearby). This is why radio triggering is often preferred.

Whether you'd be better served to go to a 3rd-party radio-based system (e.g.,Godox/Flashpoint, Cactus, Jinbei/Orlit, or Phottix) or going with Sony's own OEM flashes depends on your budget and usage. The third party gear might make more sense if you shoot more than one brand of camera or may leave your current camera system, if you need radio triggering reliability, or want to expand to larger-than-speedlight options. Sticking with OEM might make more sense if you never plan to leave the camera system you're in, and primarily use speedlights on-camera with only occasional off-camera usage, and prefer warranty repair and customer service to low-low pricetags.