Yes you can. From the search page you can open multiple space pages at once, they will open in a new tab.
If you want to book multiple spaces, in either the same venue or at multiple venues, you only need to drag your preferred date and time for each space and the multiple bookings will be added to your basket. If you do not see all your bookings in your basket, try reloading the page.
You can then move to Step 2 and add additional products and facilities for each space. In step 4 of the booking process you will pay for all bookings at once.
Note: If one of the spaces in your basket is not directly bookable, but only available on request, all the bookings in the basket will be a request and the venue will have to accept the bookings before they are finalized. You will receive a confirmation when your booking is accepted and confirmed.
Want to know more about the difference between Directly bookable and spaces bookable on request?