Side piece means something different to me, is the thing that goes into my holster on my hip.
Do you mean like a mistress? As Mister Hollinger says, any female who gives you companionship, you pay, in some form or another, so, sure, they're all mistresses.
An AMP girl you see regularly and have a semi-personal relationship with? That's an ATF, or GFE, so yea sure that's a mistress or a "side piece".
If you see her more than a few times and she remembers you and she lights up when she sees that her next customer is you instead of some shithead, yea, that's your side piece.
But remember, she has access to ten men a day, seven days a week, and you are seeing her once or twice in that period. Don't kid yourself that her once a week text sessions or her extra smiley hug when you enter her store is anything other than the business relationship. Enjoy the ride, then go home and do something else.
For me, a side piece, from what I'm reading in internet, would be like a girl you met at the grocery store who you then bang regularly or DATYO her every couple days in her husband's bed and maybe you break the headboard or something or put your sperms on her wedding ring, or dirty up her underpants before she goes home to her husband Steve. Would be anything that is sexual but 100% not financial.