Within country bond borrowing -> inter-country bond borrowin

In my base model, I have 2 economies, but they are only allowed to hold their own bonds, where:
B1 = Home-issued bonds,
B2 = Foreign-issued bonds.

In my extended model, I want to allow inter-country bond borrowing.
B1H = Home holding of Home bonds,
B1F = H holding of F bonds,
B2H = F holding of H bonds,
B2F = F holding of F bonds.

So I eliminate 2 endogenous variables B1 and B2;
but I add in 4 endogenous variables: B1H, B1F, B2H, B2F.

-> I need 2 more new equations, to balance the new model system.
-> Where should these 2 new extra equations come from?? Thanks.

In a two-ctry world the lending of one country equals the borrowing of the other. Bonds should be zero in net supply. This is very easy, check any paper with a two-country model where the only assets are internationally traded bonds.

could you share with me some papers about this?