How would one go about pulling downlines from many memberships into one list?

Leonie you don't say how many contacts you are talking about or what your current personal relationship with them is. It could be as simple as setting up a group in gmail and adding them to it, which can handle up to 500 with no cost.

The E-mail service I use, which requires Double Opt-in, allows the importing of a list.
They message is VERY clear as to WHY the are being asked to Opt-in to the New List.
Typically we have 80-90% OK the transaction..the ones that don not probably would never convert anyway.
Then manage those lists in segments.
Moving people up into lists as they respond to various Calls to Action.
We send different announcements to proved paying customers, depending on level of spend, than we send to "prospects

Seems like a good idea to me Bruce:)

Trev, log into linkedin, go to the contacts >> connections tab. Scroll to the bottom of the page past your list of contacts. Click export connections. Save as a cvs file.

Is that blackhat to you?

I am not suggesting anything blackhat. All I am saying is give the program owners reason to give you a cvs of your downlines.

I hate to say it but isn't obtaining a .cvs file of contacts rather 'black hat'
And would not that company run a risk of releasing such information
I know its information of personal down-line but to suddenly get a bogus email outside of the norm runs a risk ... give the peeps the option

Well my answer would depend on your reason for pulling them into list. You really only have two options in situations like this, and A S Kumar gave you the first one already.

The second option is a little more tricky, but will save a lot more of your list if you know how to do it. Contact the owner of the program you built your downline in, offer them a reason to give you a cvs backup of your downline from their database (if you know how to work out deals and have something of value to offer,

I agree with A S Kumar. But do bear in mind your current lists will be sensitive to any direct niche change... it really depends on how you want to manage your new list and with which topics.

Give them all a reason to subscribe to your mailing list through a Capture Page, make sure you offer something valuable as Gift