Yes, you can attach a 34-inch monitor and a 27-inch monitor to this mount. The mount supports up to two monitors with a size of 17 to 34 inches and a weight of up to 9 kg per monitor. Both monitors must support VESA mounting sizes of 100 x 100 mm or 75 x 75 mm, which is the case for most monitors. It is advisable to check the specific specifications of the monitors to ensure compatibility.