I don't understand the usage of the preposition 'with' on some website:
"The Section 8 Housing Choice Voucher Program provides rental subsidies for very low-income households who reside in privately owned rental units and pay 30% of their income towards rent. The balance of the rent is paid by the Housing Authority directly to the owner. The subsidy is tied to the family so if the family moves to another residence, the subsidy moves with them. Participants can also choose to exercise a portability feature that allows them to move to another county or state and continue to use their subsidy with another housing authority. "
I checked this dictionary:
but couldn't find a good definition. Would this:
"use their subsidy under the jurisdiction of another housing authority"
be better than:
"use their subsidy with another housing authority"
"use their subsidy (from the previous housing authority) with another housing authority's subsidy"
since after moving, the tenant would get two subsidies from two different housing authorities?
No, it doesn't say that. And it would be very unlikely to mean that. The subsidy is transferred - unless it's stated somewhere else in Section 8 Housing Choice Voucher Program that you can keep moving and adding subsidies. It doesn't sound like good or fair policy if you could do that.
But, "with" sounds like combining a subsidy with a housing authority, which makes no sense.
It sounds like that to you.
Consider this: "Doctors use antibiotics with bronchitis." It doesn't mean they combine antibiotics and bronchitis as a treatment. You could make the argument that it should be "for bronchitis" - and that might be better. But it doesn't invalidate the use of "with". There is often more than one preposition that can be used, and the context should make it obvious what is meant.