您好，... may introduce more flexibility to the current cap on the amount that local authorities can borrow against their housing stock debt.

这里的 against 的含义是（概念上）按照，参照，与……相对而言。也就是 local authorities（地方政府）can borrow against their housing stock debt.（可以依照住房存量债务作抵押而借出同等量的金额）

aginst 作介词，通常有4种用法：

1）反对：the fight against crime（打击犯罪的斗争）

2）抗击，抵御：the fight against the flooding（抵御水灾的奋斗）

3）按照，参照，对……相对：benefits weighted against the costs（按成本计算利润）

4）倚着，靠在：stood with your back against the wall（背靠着墙站立）