Hello,

By default, there is an option to connect only one filter to data source. You need to set up the Filter name property of the filter to match the Filter name property of the datasource.

However, if you want to chain more than one filter, you can use the SourceFilterName property of the Filter web part and set it to a Filter name of a the other Filter web part:

Filter A:
Filter Name : FilterA
SourceFilterName: FilterB

Filter B:
Filter Name : FilterB

Data source:
Filter Name: FilterB

Of course, by default, there is no property called SourceFilterName, so you will need to add it in the Site manager [Development -> Web parts -> General -> Filter -> Properties] and modify the code of the filter web part [~/CMSWebParts/General/filter.ascx.cs]:

private string mSourceFilterName = null;
public string SourceFilterName
{
    get
    {
       return ValidationHelper.GetString(this.GetValue("SourceFilterName"), mSourceFilterName);
    }
    set
    {
       this.SetValue("SourceFilterName", value);
       this.mSourceFilterName = value;
    }
}

The following definition needs to be added to Load_Filter method:

this.mFilterControl.SourceFilterName = this.SourceFilterName;

For more related information, I would like to point you to the following blog: Custom filter development with Kentico CMS

Best regards,
Michal Legen