Every opportunity has to be grabbed and made the most off, because if you don't take them then someone else will. There are tens of thousands of writers out there all trying to grow a career and you have to make yourself stand out from the crowd. You might overload yourself with work at first but as you grow as a writer and become more experienced, you'll get to know which opportunities are the ones to pursue and which are the ones to politely decline.
Of course opportunities very rarely appear out of thin air and the vast majority have to be worked for. Making connections, collaborations, occasionally working for free and making yourself invaluable to other media types will go a long way towards this. If you get a reputation for being helpful, polite and good to work with, the opportunities will soon flow your way. You don't need to go looking for them.
A successful writer grabs every opportunity and makes the most of it. An unsuccessful writer doesn't. Which are you?