Dear H.M.B.: Considering that mergers and acquisitions announced worldwide shot up 47% last year (total value: $3.5 trillion), their highest level since 2007, and since many of those deals are just now coming to fruition, you can be sure that plenty of other employees are in the same boat.

But even people whose employers haven’t merged will, sooner or later, have to learn the art of impressing a new management team. “For one reason or another, the average person will have 10 or more new bosses over the course of his or her career,” notes Teresa Taylor, a former telecommunications executive who now sits on a dozen boards of directors. “You can sit back and watch the change happen, or you can influence it.

“Don’t worry about being ‘too political,’” she adds. “Getting to know the new people in charge, and making a good impression on them, isn’t about politics. It’s about figuring out how you fit in now. If the idea of asking your new boss out for lunch or drinks bugs you, think of it as networking, which is really the same thing.”

Taylor speaks from experience. She was one of a large group of product managers at Qwest when US West bought the company in 2000. US West had its own product managers, so layoffs seemed inevitable. Taylor got busy making herself so valued by the new team that she got promoted to a newly created executive vice president position, overseeing all the product managers from both companies.

How did she pull that off? Taylor says these three steps worked for her:

Bring solutions, not problems. “There’s nothing worse for a new boss than to have a parade of people in her office who can describe in great detail what is wrong,” Taylor says. “Some people have truly made an art form out of defining the problem.” Don’t be one of them. It’s helpful to bring up things you believe need fixing, but only if you can identify at least three possible solutions.

Read the tea leaves. “Try to identify the needs of the new boss. If you were in her shoes, what would you want to know?” says Taylor. “There’s no question that the goals and the culture are going to change, so embrace that by observing the differences.” If possible, demonstrate that you want to be part of the change by “showing initiative and completing a project no one asked you to do,” she adds. “Often, in an acquisition, people’s first impulse is to try to hide, but that’s a mistake. Jump in. Be engaged. Pick something that you’ve always been good at, and let it shine.”

Be flexible. A merger is a good time to dust off your resume, even if you’re counting on staying. “A common practice is to have people re-interview for the jobs they’ve already got, or for other jobs that have opened up in other parts of the reorganized company,” Taylor points out. “It’s smart to be thought of as ready for any assignment, because the company and your role in it will continue to evolve, even if a particular move doesn’t seem like a great option at the time.”

That idea, too, comes from Taylor’s own career. After three years as product management chief, she got appointed head of human resources. “It seemed ridiculous to me. I was one of those people who always snickered about HR,” she says. “Here I was, a sales and marketing person, suddenly in charge of union contracts, employee benefits, and so on.” Still, she took the assignment, which “turned out to be a big part of what qualified me” for a promotion to chief operating officer two years later.

“Change is never easy. But even if you end up somewhere else in the company from where you are now and it doesn’t seem ideal, make the best of it,” she suggests. “You never know where it will lead.” Good luck.

Talkback: If you’ve ever survived a merger or acquisition with your job intact, or you ended up with a better one, how did you do it? Leave a comment below.

Have a career question for Anne Fisher? Email askannie@fortune.com.