Remove all items from an array NOT in array in MongoDB - arrays

Question

I have two collections in Mongo. For simplification I´m providing a minified example
Template Collection:
{
templateId:0,
values:[
{data:"a"},
{data:"b"},
{data:"c"}
{data:"e"}
]
}
Data Collection:
{
dataId:0,
templateId:0,
values:[
{data:"a",
value: 10},
{data:"b",
value: 120},
{data:"c",
value: 3220},
{data:"d",
value: 0}
]
}
I want to make a sync from Template Collection -> Data Collection, between the template 0 and all documents using that template. In the case of the example, that would mean:
Copy {data:"e"} into the arrays of all documents with the templateId: 0
Remove {data:"d"} from the arrays of all documents with the templateId: 0
BUT do not touch the rest of the items. I can´t simply replace the array, because those values have to be kept
I´ve found a solution for 1.
db.getCollection('data').update({templateId:0},
{$addToSet: {values: {
$each:[
{data:"a"},
{data:"b"},
{data:"c"}
{data:"e"}
]
}}}, {
multi: true}
)
And a partial solution for 2.
I got it. First tried with $pullAll, but the normal $pull seems to work together with the $nin operator
db.getCollection('data').update({templateId:"QNXC4bPAF9J6r9FQu"},
{$pull:{values: { $nin:[
{data:"a"},
{data:"b"},
{data:"c"}
{data:"e"}]
}}}, {
multi: true}
)
This will remove {data:"d"} from all document arrays, but it seems to overwrite the complete array, and this is not what I want, as those value entries need to be persisted
But how can I perform a query like Remove everything from an array EXCEPT/NOT IN [a,b,c,d,...] ?