Does aikau MultiSelectInput support more then one value?

Consider widget config:

{
    id: "MyMultiSelect",
    name: "alfresco/forms/controls/MultiSelectInput",
    config: {
        label: "My multi-select input",
        name: "assoc_myGood",
        width: "400px",
        addedAndRemovedValues: true,
        valueDelimiter: ",",
        choiceCanWrap: true,
        choiceMaxWidth: "100%",
        optionsConfig: {
            labelAttribute: "name",
            queryAttribute: "name",
            valueAttribute: "value",
            publishTopic: "ALF_CRUD_GET_ALL",
            publishPayload: {
                url: "/slingshot/datalists/lists/node/workspace/SpacesStore/dc1b9c22-b955-4e5f-9b10-2343680a15f5",
                resultsProperty: "response.datalists"
            },
            searchStartsWith: true
        }
    }
}

Values are retrived, but when it comes to select, it possible to select one value but after that all other values become disabled. E.g. only one value can be selected.

So does MultiSelectInput support select more then 1 value?

Yes, MultiSelectInput does support the selection of more than one value. See this live example on the Aikau Sandpit. I would suggest that the issue is that your optionsConfig is incorrect. Based on your other question I would say that each option is being assigned the same value which is why only one option can be selected.