Hiri supports performing various actions like moves, delete, mark as read/unread on multiple conversations.
To get to the multi select mode, simply hover over the email avatar to reveal a checkbox. Alternatively you can simply hit <space>. That will switch the top bar to multi select mode.
To select all conversations on the current page, click Select all button in the top left corner. To mark as read/unread, delete and archive simply use the icons in the top bar.
You can always drag the selected conversations to move them to Inbox, Action, FYI filters (left hand side) and to folders (right hand side).