To start I have to say there is nothing wrong with being a terminal intermediate if you are having fun and spending time and money to improve your ski technique isn't a priority or just not practical at the moment.
To get past the "intermediate plateau" the simple answer is to keep taking lessons, but know that mileage is important too. A few years ago a friend in the Mid-Atlantic and I started an online discussion about what it took to get to an advanced level for someone who could only skied about 20 days a season and didn't live in ski country. The conclusion was that while it's possible with random lessons and days on snow at small hills (PA, VA), it's a lot easier if can include a 1-week ski vacation to a big mountain. Not only can get in more mileage, that allows a few days to focus on skiing even if doing some work remotely in the evenings.
Read on for my story and more thoughts about how to improve . . .
I was a terminal intermediate for decades, from my 20s to early 50s. That meant I stuck to groomers on trips out west (not every winter), which was my only skiing for quite a while. Happens with you are working and married to a non-skier. I'd skied for two seasons in middle school (straight skis, lace up boots) because I was having a grand time at North Country School in Lake Placid, which has a rope tow ski hill on campus. Loved it but didn't ski at all for ten years since my family moved from NYC to North Carolina.
Before I started taking lessons about 10 years ago, I could make it down an ungroomed slope or a groomer with chopped up snow but it was a lot of work and there was a lot of stopping along the way to recover and reset for a few more turns. I was an adventurous advanced intermediate. My daughter was a better skier than I was by age 10 since she started with ski school at age 4, even though we were only skiing 10-15 days working around a school schedule. It was eye-opening when I experienced the difference between an instructor with PSIA Level 3 certification and/or 20+ years of teaching experience and the usual instructors teaching intermediate group lessons. By the time I was 60, I was skiing terrain I never expected to ever touch. Still expect to keep improving for at least another decade. Maybe longer given what my ski buddy has learned from instructors in his late 60s, and he was an advanced skier in high school.
The other factor that really helped was finding a ski buddy who was both a much better skier and very patient and willing to be a sweeper. That meant I could do "adventure runs" during trips out west. Having a sweeper means there is someone behind you who can help if you fall, makes it easier to go a little faster and make a few more turns before stopping on a more challenging run. What's challenging changes with conditions and improving ability. Could be a steeper groomer, or a short section of bumps on the side of a groomer, or some run off-piste where there isn't a way to bail.
The reasons I wanted to get off groomers and feel more confident skiing any black terrain shifted as I had the opportunity to ski more often and take more trips out west. The top three below is how I started. #3 about powder is because I experienced one powder run (boot deep) on Ballroom in 8th grade with an instructor during a trip because a friend invited me for a week. I never forgot the feeling. #4 and #5 are why I've kept taking semi-private lessons and going to Taos Ski Weeks in recent years. I didn't understand why learning to ski bumps (not zipper-line) was so useful until after a couple seasons of lessons with L3 instructors, both at my home hill and out west.
1) stay better than my daughter . . . didn't work, she was better by age 10
2) get away from crowded blue trails in the southeast, mid-Atlantic, or northeast
3) learn to ski deep powder
4) learn to ski powder in trees, which meant learning to ski bumps first
5) make it easier to explore a new ski area/resort because no worries about getting into terrain that would be too difficult