Visual object tracking is of great interest in many applications, as it preserves the identity of an object throughout a video. However, while real applications demand systems capable of real-time-tracking multiple objects, multi-object tracking solutions usually follow the tracking-by-detection paradigm, thus they depend on running a costly detector in each frame, and they do not allow the tracking of arbitrary objects, i.e., they require training for specific classes. In response to this need, this work presents the architecture of SiamMT, a system capable of efficiently applying individual visual tracking techniques to multiple objects in real-time. This makes it the first deep-learning-based arbitrary multi-object tracker. To achieve this, we propose the global frame features extraction by using a fully-convolutional neural network, followed by the cropping and resizing of the different object search areas. The final similarity operation between these search areas and the target exemplars is carried out with an optimized pairwise cross-correlation. These novelties allow the system to track multiple targets in a scalable manner, achieving 25 fps with 60 simultaneous objects for VGA videos and 40 objects for HD720 videos, all with a tracking quality similar to SiamFC.