As a matter of fact, the input text node from the dashboard always behaves like you want by default. It will not neglect the second and following msg.payload coming in.
However, the msg.payload type has to match the mode type from the dialog configuration dialog.
If they don't math then msg.payload will be "ignored" as you said. For instance, if you configured the mode type as number and send a msg.payload of string type then this msg.payload will not be displayed in the input box.
Below flows shows how it works when payload type matches (first flow) and when it does not match (second flow).
Flows:
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