I have a quite energetic, 1.5 year old female cat, who used to live outside until 6 months old.
We get along nicely, and I try to have play sessions with her 2-3 times a day for at least 5 minutes - it's usually two 5-minute and two 10-minute sessions every day. I have to note that these are not on a fixed schedule; the cat does not know when to expect playtime at all, and a couple of times per month there might be a day with no play sessions at all.
The thing is - no matter how much she plays, it never seems to be enough for her! This makes me a little skeptical:
Is she getting the fun, exercise and stimulation she needs? Can there be other reasons why a cat would like to play much more than usual?
There already is quality and variety in her playtime, so I doubt that new toys are the answer here. Is it possible at all that a new kitten in the household would help her? Could she just be lonely and looking for ways to spend more time with me? Any other ideas what this behaviour could indicate?
Here's some more info on her playing and asking-for-play behavior:
I often alternate between toys from session to session, give her challenges, encourage her to run around chasing the toy and the such. She also likes to play hide-and-seek and peek-a-boo, although string toys are her favorite. She loves it all (sometimes she even purrs while playing). Most of the play sessions are very energetic.
I've never seen the slightest indication that she gets tired when playing. Sometimes she hides and waits for the moment the toy is not moving before attacking, but I believe that's just good hunting technique she learned while outside, not an indication of tiredness.
The more often I play with her, the more playtime she's going to ask for. If I don't play with her for a couple of days, she might not ask at all, although she'll still engage joyfully as soon as I grab a toy.
How she asks for playtime: Trying to lure me to the living room when I'm not there by meowing expectantly, coming to my door then running away, showing/bringing me a toy, rubbing on my legs to get my attention before making play gestures with her paws, lying on her back while playing with an imaginary toy hanging above her.
She does not get aggressive when not played with, and is not aggressive in general. She never breaks things or attacks clothes/furniture or other items.
She always respects my privacy; won't wake me up at all, won't bother me again if she's tried and I'm busy. Will only try to call out for me a couple of times and stop if she fails.
Playing is the activity we spend the most time together on: she does like to be petted, but less frequently than your average house-cat, and does not usually like to be held.