Systems-of-Information Systems (SoIS) refer to collections of software systems that became able to deliver innovative functionalities as well as meet new business opportunities due to novel connections formed with information systems. The software architecture of SoIS plays an important role in their success since they are frequently associated with essential quality attributes, such as sustainability, performance, and reliability. Aiming to study the software architecture of SoIS, additional types of models can be explored for predicting its runtime behavior and structure. Through examples with formal and semiformal notations, we discuss the advantages and limitations of selected techniques for the description of high level models of SoIS, namely SysML, SosADL, and DEVS. Finally, we outline directions for future work on tailored architectural models for practitioners and researchers dealing with SoIS analysis and design.