P.s.: The added data should be and will be frequently searched/filtered and optionally will be returned with the basic responses.

So after many trial and errors there is no solution to the problem without very ugly hacks.

Finally what I've settled with is saving the extra data and create a new CreateTeamRequest using the id from the extra data entry. To cancel the request so it won't try to create the team twice, I have set a scriptError with the original response and copied that into the scriptData in the CreateTeamResponse.

// ====================================================================================================
//
// Cloud Code for CreateTeamRequest, write your code here to customize the GameSparks platform.
//
// For details of the GameSparks Cloud Code API see https://docs.gamesparks.com/
//
// ====================================================================================================

var data = Spark.getData();


// TODO: eval scriptData
var scriptData = data.scriptData;


// save data
var extra_data = Spark.runtimeCollection("teamExtraData");
extra_data.save(scriptData);

// give id to team and that's it
data.teamId = scriptData._id["$oid"];

// another request as we need to know if the team can be created
var response = Spark.sendRequest({
  "@class": ".CreateTeamRequest",
  "teamId": data.teamId,
  "teamName": data.teamName,
  "teamType": data.teamType,
  "scriptData": {"ez":"valami"}
})

if( response.hasOwnProperty("error") ) {

    // remove extra data
    extra_data = Spark.runtimeCollection("teamExtraData");
    extra_data.findAndRemove({"_id": {"$oid": data.teamId }});

    // couldn't create team
    for (var property in response.error) {
        if (response.error.hasOwnProperty(property)) {
            Spark.setScriptError(property, response.error[property]);
        }
    }

} else {
    Spark.setScriptError("skip_request", response);
}

Spark.exit();

// ====================================================================================================
//
// Cloud Code for CreateTeamResponse, write your code here to customize the GameSparks platform.
//
// For details of the GameSparks Cloud Code API see https://docs.gamesparks.com/
//
// ====================================================================================================

var data = Spark.getData();

// save original response
var orig_response = Spark.getScriptError("skip_request");

// remove fake error with original response
Spark.removeScriptError("skip_request");
if(Object.keys(data.error).length === 0 && data.error.constructor === Object) {
    Spark.removeAllScriptErrors();
}

if( orig_response !== null ) { 
    Spark.setScriptData("response", orig_response);
}

Spark.exit();

 This is working but very ugly and error prone. Also it renders your framework absolutely unnecessary 'cause this could be a custom request.

The preferred way would be something like:

//
// request script

var scriptData = Spark.getData().scriptData;

var extra_data = Spark.runtimeCollection("teamExtraData");
extra_data.save(scriptData);

Spark.setData("teamId", scriptData._id["$oid"]);

//
// GS creates team with the set id and gives normal response
//

//
// response script with teamId and scriptData still set

if( Spark.hasScriptErrors() ) {
  var data = Spark.getData();
  var extra_data = Spark.runtimeCollection("teamExtraData");
  extra_data.findAndRemove({"_id": {"$oid": data.teamId }});
}

 Much cleaner and response can be processed normally by GS API and our code as well.

bump - I'd like to be able to set a public/private flag on a team when it's created and can't come up with a solution other than what RwB World has suggested above.