Rather than adding inputs with the add input button (which adds them to the fieldset element), edit the source of the dashboard and add the inputs in another panel in a row (as @gcusello suggested)
<row> <panel> <input token="..."> </input> </panel> </row>
as me and @ITWhisperer said, you can create a dedicated panel containing the inputs (e.g. in the third row), then you can use those tokens in more panels, you have only to use a different name for the tokens.
I hint also to explore the possibility to divide your dashboard in mode tabs putting inputs and panels in each tab; this is described in the Splunk Dashboard Examples App (https://splunkbase.splunk.com/app/1603/) in the Link Switcher example.
you can create fieldset in the dashboard header or in a panel.
I don't completely understand your requirement: you want to have in one dashboard more panels and more inputs, is this correct?
You could create:
Why don't you put all inputs in the dashboard header? it's easier and more readable.
are you sure that your dashboard continues to be usable and not too complicated?
I have multiple inputs but some inputs needs for first row (API Counts with multiple panel) and some inputs need for second row(Event Counts with multiple panel) within the same dashboard.