According to page 22 of the manual, you can transfer Yamaha SFF style files to the PSR-A300's memory. I assume they must be SFF1 style files, not SFF2 style files. There are free utility programs on Jorgen Sorensen's website for working with Yamaha style files, including a program for converting SFF2 style files to SFF1 style files:
Style Format 2 Converter - The Unofficial YAMAHA Keyboard Resource Site
www.jososoft.dk
Page 67 says that you must use the Yamaha Musicsoft Downloader program to transfer the style files from your computer to the keyboard's memory. It does not say how many style files the keyboard's memory can hold.
Note that since the PSR-A300 has MIDI In/Out ports rather than a USB To Host port, you will need to use a decent quality USB-MIDI interface to connect the keyboard to your computer, such as Yamaha's UX16 interface. Also note that the Yamaha Musicsoft Downloader will probably need to recognize the connected keyboard, so it's likely that you absolutely
must use Yamaha's UX16 interface-- as opposed to some third-party USB-MIDI interface-- so that you can install the Yamaha USB-MIDI driver as well.
You can "register" a single style file as Style Number 136 by using the "Style Register" function that's mentioned on page 61-- so even though you can transfer multiple style files to the keyboard's memory, you may use only one of them at a time.