In fact, when the Button element is in the "Multiple presses" mode, it does register all presses. However, the "Triggered Button" and "Triggering Time" properties are singular and show statistics of the last press only. In order to record all button presses with the Button element, you need to collect the button presses manually. Consider, for example, this way:
1) Declare a string variable in Header snippet:
2) Reset this variable in the 'After Onset' snippet of your 'response' event (in which the Button element is located):
3) Accumulate every new button press in the 'Triggered' snippet of the Button element (the snippet is automatically called on every new button press):
Finally, you can record the resulting PressedButtons string into Data Report. In the similar way, was you can record button press times, accumulating values of the "Triggering Time" property.
There is also another, easier, way to record all button presses during one or multiple events. You can use Key Logger element, which automatically records a list of all button events within the parent event. Every line in that list includes a button name, event type (press or release) and event time. If you create a proxy variable linked to the "Key Log" property of the Key Logger element, you can access the collected list and record it (e.g.with "Reporter" element).
Normally, you should use the Key Logger element for passive logging of button events. The Button element should be used, when you need to process button presses in real-time, e.g. in evaluation of a participant's response.