Seems a bit crazy 
For the crazy request - crazy solution! 
db.test.aggregate([
{
$group: {
// specify group-by fields here
_id: {
x: '$x',
y: '$y',
z: '$z',
},
docsEntries: {
$push: {
$objectToArray: '$$CURRENT',
},
},
},
},
{
$addFields: {
docKeysList: {
$map: {
input: {
$arrayElemAt: ['$docsEntries', 0],
},
in: '$$this.k',
},
},
},
},
{
$addFields: {
// gather fields, values of which we will sum-up
filteredKeyList: {
$filter: {
input: '$docKeysList',
cond: {
$not: {
// specify ignored fields, that you do not want to calculate
// at minimum, here should be _id and grouping keys
$in: ['$$this', ['_id', 'x', 'y', 'z']],
},
},
},
},
},
},
{
$addFields: {
// collect all entries (values of same key from all docs in the group)
// in the single array
groupedEntries: {
$map: {
input: '$filteredKeyList',
as: 'filteredKey',
in: {
$reduce: {
input: '$docsEntries',
initialValue: [],
in: {
$let: {
vars: {
targetDocEntry: {
$filter: {
input: '$$this',
as: 'docEntry',
cond: {
$eq: ['$$docEntry.k', '$$filteredKey'],
},
},
},
},
in: {
$concatArrays: ['$$value', '$$targetDocEntry'],
},
},
},
},
},
},
},
},
},
{
$addFields: {
calculatedEntries: {
$map: {
// we need to ned to return { k, v } for each key, so we can
// transform it to single object with custom prop names
input: '$groupedEntries',
as: 'groupedEntry',
in: {
k: {
$let: {
vars: {
item: {
$arrayElemAt: ['$$groupedEntry', 0],
},
},
in: {
// here the custom prop name is calculated
// feel free to change the logic if needed
$concat: ['total_', '$$item.k'],
},
},
},
v: {
$reduce: {
input: '$$groupedEntry',
initialValue: 0,
in: {
$add: ['$$value', {
$convert: {
input: '$$this.v',
to: 'double',
// Change NaN to 0 for onError prop,
// if your props can contain various value types
// and you cant to calculate only number values
// for every document field
onError: NaN,
onNull: 0,
},
}],
},
},
},
},
},
},
},
},
{
$addFields: {
results: {
$arrayToObject: '$calculatedEntries',
},
},
},
{
$project: {
results: true,
},
},
]).pretty();
And for the following documents:
db.test.insertMany([
{ x: 1, y: 1, z: 1, propA: 5, propB: '5', propC: 't5' },
{ x: 1, y: 1, z: 2, propA: 10, propB: '10', propC: 't10' },
{ x: 1, y: 1, z: 2, propA: 15, propB: '15', propC: 't15' },
]);
The aggregation will return:
[
{
"_id" : {
"x" : 1,
"y" : 1,
"z" : 1
},
"results" : {
"total_propA" : 5,
"total_propB" : 5,
"total_propC" : NaN
},
},
{
"_id" : {
"x" : 1,
"y" : 1,
"z" : 2
},
"results" : {
"total_propA" : 25,
"total_propB" : 25,
"total_propC" : NaN
},
},
]
The solution is not ideal and can be improved, but that is another crazy story 
I made this just to proove, that this is possible with Mongo v4.2.