Dating a narcissist who wants to put efforts to change. He's let me down majorly twice. Is there room for change or am I hoping for too much?

Anonymous
LONG STORY
My boyfriend (M, 31) and I (F,23) have been together for 9 months. There were many red flags I ignored initially. He was so invested in me (or so I thought) that he said he wanted to marry me just as we were getting together. Little did I know that all this was part of the love bombing phase

1. He had a female friend and their boundaries were WAY OFF. When confronted, he agreed that they had some sort of a fling in the recent past (but I don't know how long that actually went on)

Few months down, he stopped loving me the way he used to, would give me the silent treatment a lot, and I'd start wondering if I should be better and I'd ask him how he'd like me to react the next time. The whole phase of being devalued and unloved got me clinging on in hopes that if I tried harder, maybe I'd be worthy of his love

2. I noticed him act weird around his phone. His brother's girlfriend pointed out that I should watch out. He gave me the phone thinking I wouldn't take a look but at that point, I'm not proud of it, I took it and my heart sunk after all that I saw. All his half truths, lies, women I never knew that existed in his life talking cheesy stuff. The biggest heartbreak- He was flirting with the gym instructor using the SAME things he used with me and this had happened just as we had gotten together. We met at the gym

Currently, he says his biggest issue is that I've unearthed a side of him he wanted to keep a secret. He agrees to all of this and wants to change. There's also the side of him where he is extremely controlling and wants his way with the way I dress, take pictures, the people I talk to and even the way I express myself. He'd shame me badly for doing something completely normal and go behind my back and do the same thing. Somewhere I feel he is just trying his best and that I need to be patient as I love him a lot, but it is destroying everything that I am. I feel lost, drained and hurt
Dating a narcissist who wants to put efforts to change. He's let me down majorly twice. Is there room for change or am I hoping for too much?
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