In many applications of optical coherence elastography (OCE), it is necessary to rapidly acquire images in vivo, or within intraoperative timeframes, over fields-of-view far greater than can be achieved in one OCT image acquisition. For example, tumour margin assessment in breast cancer requires acquisition over linear dimensions of 4-5 centimetres in under 20 minutes. However, the majority of existing techniques are not compatible with these requirements, which may present a hurdle to the effective translation of OCE. To increase throughput, we have designed and developed an OCE system that simultaneously captures two 3D elastograms from opposite sides of a sample. The optical system comprises two interferometers: a common-path interferometer on one side of the sample and a dual-arm interferometer on the other side. This optical system is combined with scanning mechanisms and compression loading techniques to realize dual-scanning OCE. The optical signals scattered from two volumes are simultaneously detected on a single spectrometer by depth-encoding the interference signal from each interferometer. To demonstrate dual-scanning OCE, we performed measurements on tissue-mimicking phantoms containing rigid inclusions and freshly isolated samples of murine hepatocellular carcinoma, highlighting the use of this technique to visualise 3D tumour stiffness. These findings indicate that our technique holds promise for in vivo and intraoperative applications.