Welcome, Ron!
I agree with panos that playing along with your many MIDI song files is the way to go for what you want to do.
Styles are more useful for playing particular types or genres of music where the backing or accompaniment consists of one or two recurring loops, with the exact notes and key changes being controlled by the chord progressions that you play. (A Yamaha style file can contain up to four loops or "Main" sections, along with "Fill In," "Intro," and "Ending" sections, but your PSR-E413 will be able to access only two of them, the "A" and "B" variations.)
As for using MIDI song files, you should be able to load/import a given file into a DAW or other program. You can then either remove the specific channel(s) whose part(s) you want to play yourself, or rearrange the channels as needed so you can more easily use your PSR-E413's "Track Control" buttons to mute the part(s) you want to play yourself. The easiest ones to mute are channels 1 and 2, but I think you can use the "Function" menu to specify which channels you want to associate with the "Right Hand" and "Left Hand" parts, and then use the first two "Track Control" buttons to mute those parts as desired-- although I've never tried it myself to verify that it works that way.
Note that since the PSR-E413 doesn't contain a "USB To Device" port, you won't be able to insert a USB drive that has all of your song files and style files on it, so you'll need to connect to a computer via the "USB To Host" port and use Yamaha's free Musicsoft Downloader program-- or their free MusicSoft Manager app if you're using an iPad, iPhone, or iPod touch-- to transfer the desired songs to your computer's internal memory. Then you can select a song and play it, or in this case play along with it.