Associations, particularly small associations, tend to suffer from a lack of resources, aka "that's a great idea, but we don't have any money for it." Which can have a seriously negative consequences on impact and what the organization is able to accomplish.
One way to address this is through creating a network of allied organizations.
So how do you do that?
The first step is research. You need to figure out what organizations have similar enough, but not identical, missions and audiences. You're looking to compliment each other, not to compete. And you want organizations that are at a similar level of influence. Too many orders of magnitude bigger or smaller, and the power dynamic gets out of whack, which can make it hard to find mutual benefit.
The next step is to think through what mutual benefit might look like. What can you offer that they might want? What do they offer that you want? Can you create packages of roughly equivalent value? Possible areas of interest might include discounts for members on programs, products or services, exhibit booth swaps, conference speaking session swaps, mailing list swaps, ad swaps, article swaps, guest blogging, joint products, advocacy alliances, joint workshops or webinars, applying for research grants together...think through everything both organizations offer and look for places you could work together.
Third, you have to make contact. This is where things like LinkedIn can come in handy. Look for a path, ideally, to the person who seems most likely to be able to say yes or no, but also realize that the first person you're able to connect with might not be the right person to negotiate a relationship. Don't be afraid to pick up the phone, and do be persistent but don't be obnoxious.
Assuming you find the person with the appropriate authority and willingness to make a deal, the next step is to negotiate something that will work for both of your associations. You want both organizations to have an initial positive experience, so your beta should be structured to make that as likely as possible, which means start small. But brainstorm big. Assuming your first test goes well, you want to have ideas waiting in the wings to expand the relationship.
Lather, rinse and repeat with additional organizations, and watch your association's sphere of influence expand exponentially.