Yes it is possible Nick! Inside the Umbraco.Form.js you can add additional fields in the setting section of questions.

You need to modify the following code:

    formResource.getPrevalueSources().then(function (resp) {
        vm.prevaluesources = resp.data;

        formResource.getAllFieldTypesWithSettings().then(function (resp) {
            for (var i = 0; i < resp.data.length; i++) {
                // add new setting here
                resp.data[i].settings.push({ name: "Extra Setting", alias: "extraSetting", description: "Enter in your message", prevalues: Array(1), view: "/App_Plugins/UmbracoForms/Backoffice/Common/SettingTypes/TextField.html" });
            }

            vm.fieldtypes = resp.data;
            vm.ready = true;
        });
    });





    function openFieldTypePickerOverlay(field) {

        vm.focusOnMandatoryField = false;

        vm.fieldTypePickerOverlay = {
            view: "/app_plugins/UmbracoForms/Backoffice/Form/overlays/fieldtypepicker/field-type-picker.html",
            title: "Choose answer type",
            hideSubmitButton: true,
            show: true,
            submit: function(model) {
                //add new setting here
                model.fieldType.settings.push({ name: "Extra Setting", alias: "extraSetting", description: "Enter in your message", prevalues: Array(1), view: "/App_Plugins/UmbracoForms/Backoffice/Common/SettingTypes/TextField.html" });

                formService.loadFieldTypeSettings(field, model.fieldType);

                // this should be removed in next major version
                field.removePrevalueEditor = true;

                vm.fieldTypePickerOverlay.show = false;
                vm.fieldTypePickerOverlay = null;
            }
        };

    }