I think lots of UK/US pairs will satisfy this, e.g. FHI and MIRI. (I think I (in the UK) can make tax-deductible donations to FHI, but not MIRI; and I think Americans have it the other way around.)
Americans can make tax-dedutible donations to FHI through Americans for Oxford: http://www.fhi.ox.ac.uk/support-fhi/
I had an idea a while ago, which sounded simple to me, but searching with certain keywords did not yield appropriate results, so am presenting it for discussion to LW . Please inform me if something like this is already in existence. Please inform if I need to cross post it on effective altruism forum also, or they share enough users with LW and it need not be repeated.
Introduction
Two persons A, B living in different tax jurisdictions I and J respectively, want to contribute to organizations M and N qualifying for tax exemption in the other person's jurisdiction. i.e. M qualifies in J and N qualifies in I. For the purpose of this demo, lets consider they intend to contribute the same amounts.
They "swap" their charities and produce receipts to the effect from the respective organizations.i.e. A contributes to N and B contributes to M.
This helps them gain 10% to 20% more money when compared to contributing to their preferred charities which do not qualify.
So, the idea is to create a website where people can post such an intent, to contribute to cross-national charities and can reliably present receipts that will be acceptable to all concerned.
The main uses i envisage for such swaps would be science supporters in the developing world wanting to contribute to research happening in the developed world swapping with EA's wanting to gain a bigger bang for their buck in the developing world. This potentially reduces the need for a lot of charities to seek out tax exemption in multiple jurisdictions.
Avenues for further research
Question on the basic idea
Logistics questions