Adding Fields to an existing Array - mongodb

Question

I have another problem to solve here. Thinking in arrays sometimes could be very challenging. Here is what I am lined up with. This is what my data looks like: -
{
"_id": { "Firm": "ABC", "year": 2014 },
"Headings": [
{
"costHead": "MNF",
"amount": 500000
},
{
"costHead": "SLS",
"amount": 25000
},
{
"costHead": "OVRHD",
"amount": 100
}
]
}
{
"_id": { "Firm": "CDF", "year": 2015 },
"Headings": [
{
"costHead": "MNF",
"amount": 15000
},
{
"costHead": "SLS",
"amount": 100500
},
{
"costHead": "MNTNC",
"amount": 7500
}
]
}
As you can see, I have a list that has a whole bunch of sub-documents.
Here is what I want to do .. I need to add more elements to this "Headings" list which should be : -
{
"costHead": "FxdCost",
"amount": "$Headings.amount (for costhead MFC) + $Headings.amount (for costhead OVRHD)"
}
I am unsure as to how to produce the above. Here are some challenges: -
I can addToSet the new subdocument I wish to add but the problem is addToSet can only be used in the group stage - which would be expensive (unless of course there is no other way).
Even if I use addToSet, I always have to use the $ operator to refer to elements that I read from my JSON file. Now the element I am trying to add here (costHead: FxdCost) is not present in my JSON file and hence I cannot use the $ operator.
Does anyone have any advice on how to go about this. This is after all basic ETL.