It's happened in the past a couple of times with different SP's, mostly regulars, lots of different reasons why it occurred, a few times it was because we were enjoying the session and we both lost track of time,
other times times SP asked me to stay and have a glass of wine and unwind or cuddle and chat, it has sometimes lead to more action but that was the exception not the rule. I've mostly seen Indies so, they handle their own schedule and decide how they want to proceed, as for compensation, I always try and offer more if possible (for regulars I take my wallet with me, for new meetings I take only the donations nothing else) or take note to offer something on next meeting. I've had SP's tell me the extra bit is on the house, I still try and show my appreciation even if it's just by setting up a return visit sooner than planned or bottle of wine or something on future visit.
One rarity has been the conscientious SP who sees the end of the session approaching and knows you're close and who insists you stay a few minutes more to make sure to get your SOG, again rare but I say a blessing for the few who have your SOG at heart, again they should be tipped nicely or offered a small token of gratitude on following meetings and visited regularly to know they are appreciated as damn that if that hasn't become as rare as hen's teeth.
I've had a couple of old school Indy MP's, usually the Eastern European set sometimes the Québécoise, keep me to have a convo or glass of wine/water, that's time off the table post session, I usually check in after a little bit to see if they've got another session and if I'm into the conversation then I'll stick around but I am aware that it's at their whim. This doesn't happen much and rarely in salon settings, unless it's the person running it. There was Bernadette in NDG who could hold a conversation, there was also another MP in NDG who would pick up our convo topics from the last time, I discovered later she kept notes in a little journal about each guy, helped for tailoring the session but also who to avoid too I suppose. That's something you don't see much anymore.
I have never tried to mooch free time or extend session without compensation or insist if I haven't popped, that's a shithead move and they deserve to be compensated for their job no matter how well they might maintain the illusion that it's not.