[TweedleDee199]

Ditto everything that has already been said, ESPECIALLY attending philanthropies. I can't think of anything that has my won my chapter's allegiance quicker than a fraternity showing up in full force to our event. If your brothers show up in letters with a smile girls will notice (one house came to our event this year in matching shirts. It was humanly impossible not to notice them.) Likewise, if you get paired with a sorority for any sort of competition be the BEST partners you can be. There are plenty of "top" houses on my campus that aren't worth squat as partners and nothing is more frustrating. A couple of other things that haven't been touched on as much yet...
1. Do you ever plan community service events with sororities? This is a fairly common thing on my campus and seems generally successful at improving chapter relationships. It's a nice way for people in relationships to meet members in other chapters in a "friendzone" setting and everyone has hours to get done anyways. My boyfriend is the service chair for his chapter and has made a point to arrange things with sororities that they're not on great terms with as a way to gradually build up ties. The last one led to the group all going out to dinner together afterwards. Also, if you can build up a reputation of being reliable and always sending a solid number of guys then sorority service chairs will pick you every time over chapters that are "fratty" but flaky.
2. How do you interact with other campus leaders? Do you have anyone on IFC Council? Is your president close with any of the other presidents? Close ties with other social chairs is great, but I've noticed that it's common for chapter to to chapter relations to happen from the top down on my campus. It's always interesting to see who mixes with who after the President\ IFC & Panhel Council retreat. Now don't get me wrong, a chapter leader should never force their brothers\sisters to mix with someone, and if the chapter is deadset against it they probably can't anyways. But more than once I've seen a leader come back to a chapter and say "This weekend I met the President of XYZ. He\she was awesome, why don't we ever hang out with them?" That endorsement can be enough to get a chapter to give you a chance, if only by starting out with something small like a service event or a dinner.
3. Oregon is big on dinner exchanges. Social chairs will coordinate and decide who is hosting. Our chapter sizes are on the larger side so it's by no means an all-house event . Due to our smaller dining room we usually go over to the fraternities. We'll send around 30 girls and bring desert if they're providing dinner. Sometimes they have cheesy themes like "boardgame" night, trivia night, etc. These almost universally lead to a function with the chapter afterwards.
4. Come recruitment time offer LOTS of encouragement and don't be afraid to volunteer to be guinea pigs for sororities during work week. I can't speak for everyone but when a fraternity stepped up to do that for us this year my chapter was THRILLED for another opportunity to practice conversation. Sorority women put an inordinate amount of work into recruitment and anytime fraternity men show an appreciation for that, be it with cookies and nice card or just some words of encouragement, we notice.
5. People above are right in that a new member pledge class only thing would be hazing (at least on my campus) but whenever possible try to put your new members on display and encourage them to get to know other new members. It's easier to show new additions to the Panhellenic world that you're nice guys worth socializing with than it is to change the minds of upperclassmen.
Good luck!