I'll echo the fact that large shifts in pay typically come with a change in company or position.
Had a MAJOR bump (15k - 38% increase) when I got my degree with the same company. I was still below industry average for my skillset, experience, and position. I left there and bumped up 20k (36% increase) at another company with a similar position. That company was a crapshow, moved to an ESOP company and took as base pay hit of 5k (7% decrease), but got a bonus plan that put me another 25k up (33% increase) on yearly compensation. With ESOP options, Bonus, and Salary I'll be just over 60k increase in total compensation from the first company. This is all within about 4 years time, and has been a major roller coaster for us to deal with the whack-a-doo cashflows it's created.
First company in the above story would have a performance review each year, and your pay rate was reevaluated. It had the possibilty of going either up or down based on performance. I saw several people have reductions in pay there, and several with increases. Was an odd system, but was done decently well. Of course like everything else in life it was light rewards, and heavy penalties. I had 3-5% yearlies before the big jump with my degree. Second company I didn't stick around long enough to find out how they dealt with that. new company is awesome. ESOP and bonus is based on company performance. Bonus can be as high as 40% of base pay. Salary is individual performance based. My review came around about 7mo into employment here, and the boss went to bat for me to get a raise, which he says is somewhat unheard of. The company overall is excellent, and I hope to be here for quite some time. Most likely won't change positions (I'm in R&D which only has 3 people on the team, and the head guy has been here for 15yrs with another 20+ to work. I'll retire before I get the tenure to run the department, and there are no lateral moves to be made), so it's most likely incremental raises for me from this point on.
Overall, when looking for this position....I will say that the team and "fit" I was moving into was far more important than the money. I had 3 offers within a week of each other, and the money was similar between them all. The final decision came down to how I would fit in the team, and what work I would be doing. I suspect at this level, future decisions will be made on the same premise. I've moved above the "I just need a job" mentality, and it's honestly a nice place to be. I hope I can get my boys into this position as soon as possible when they are ready to start working. Whether that is a college degree, trade school, apprentice program, or whatever that looks like. Being able to wake up in the morning and not dread the day ahead is where it's at.