Can laptop read two external hard disks together

It really should see them both at the same time, I do it all the time on much older equipment. Does it not even detect the second drive when you plug it in? Can you see it in My Computer but just does not open? Check Device Manager when you plug in the second drive, see if there is anything in there in an error state.

A driver update may fix it, maybe a BIOS update. Check online for updates to the system.

It may be a drive letter conflict.
Plug both of them in, then right click on "computer" select manage.
From the list on the left, select disk management. '
From that point, let us know if you can see both hard drives in the list that shows up. If you can, select the one that isn't showing up in "computer" and right click it. From the popup menu, you can assign a new drive letter to it.

Hope that helps, and welcome.