If there is a role that you particularly want to do, then the fact that you’re over-qualified may not matter to you. Be aware though, that employers may question your ambition, whether you are going to want to stay in the role for very long, and whether they can afford you. By all means cast your net wide, but bear in mind that lots of rejections can be hard to take, so it’s better to try to apply for roles that employers can see are a good fit for your skills, abilities and qualifications.
There is, as sometimes employers and interviewers can lack the confidence or foresight to hire the best talent available. However in this climate with so many talented people on the market, attitudes are changing and employers are raising the talent bar. Impress with the added value you offer and good luck!