Building business relationships is an important aspect of anyone's career. Many opportunities exist to meet new people at events, through referrals, online, etc. Focusing on the right relationships will go a long way.
Some people want to meet as many people as they can. You can find some of these people on LinkedIn. They call themselves "LION", which stands for LinkedIn Open Networker. For most people, quality versus quantity is more important.
By focusing on building less relationships, you will be able to really get to know these people. You will have more time to provide your own value and assist one another.
In reality, we each only need a few "power networkers" who have access to other's who we would iike to meet. As long as you build quality relationships with power networkers, they should have no problem making an introduction when needed.
Spend more time seeking out a few quaility relationships. Or spend the time nurturing some of the relationships that you already have in your network.
Over time you will build a high quaility network that you can leverage for all of your business needs. When this happens, people will seek you out and want you to be one of their high quality relationships.