I'm not sure whether it's helpful for your situation but the way I've seen this succeed in the past is to bring more people in while you're already there.
Big consulting firms do it, and do it badly, and get a bad reputation for it (but then keep getting hired back anyway), but if you do it well, it can work out fine.
My suggestions:
1) When you're on site somewhere keep an eye open for areas where one of your hired-guns could help solve a problem the client has.
2) Don't bring someone on just because it helps your company, only do it if you really believe it is in the client's interests.
3) Only bring in people you really trust, getting this wrong is deadly.
4) Be willing to make little or no money on it at first - this is primarily about marketing, not immediate income. But make it clear to the client that it's a special price and it may go up next time. Generally I find that the best angle is either to say "I think they can really provide value here, give them a trial and I can bring them in at 25% off their normal charge rate" or "Because you've been a great client, I can do a special deal this time, so you can see what else we have to offer".
5) Make sure you represent them as one of your people, not a freelancer. If they're good you want the client to come back to you and ask for them again, and not to think they can go direct.
Big consulting firms do it, and do it badly, and get a bad reputation for it (but then keep getting hired back anyway), but if you do it well, it can work out fine.
My suggestions:
1) When you're on site somewhere keep an eye open for areas where one of your hired-guns could help solve a problem the client has.
2) Don't bring someone on just because it helps your company, only do it if you really believe it is in the client's interests.
3) Only bring in people you really trust, getting this wrong is deadly.
4) Be willing to make little or no money on it at first - this is primarily about marketing, not immediate income. But make it clear to the client that it's a special price and it may go up next time. Generally I find that the best angle is either to say "I think they can really provide value here, give them a trial and I can bring them in at 25% off their normal charge rate" or "Because you've been a great client, I can do a special deal this time, so you can see what else we have to offer".
5) Make sure you represent them as one of your people, not a freelancer. If they're good you want the client to come back to you and ask for them again, and not to think they can go direct.