Seems like you are using AT 2.x so you should be able to pass an optional 3rd param into getOffers with the parameters (profile or mbox) that you need for that single call. You would need to call your data provider prior to running the code below and pass some vars around.
adobe.target.getOffers({
request: {
execute: {
mboxes: [
{
index: 0,
name: "first-mbox"
},
{
index: 1,
name: "second-mbox",
parameters: {
a: 1
},
profileParameters: {
b: 2
}
}
]
}
}
});
