LHC experiments are now in Run-II data taking and approaching new challenges in the operation of the computing facilities in future Runs. Despite having demonstrated to be able to sustain operations at scale during Run-I, it has become evident that the computing infrastructure for Run-II already is dimensioned to cope at most with the average amount of data recorded, and not for peak usage. The latter are frequent and may create large backlogs and have a direct impact on data reconstruction completion times, hence to data availability for physics analysis. Among others, the CMS experiment is exploring (since the first Long Shutdown period after Run-I) the access and utilisation of Cloud resources provided by external partners or commercial providers. In this work we present proof of concepts of the elastic extension of a CMS Tier-3 site in Bologna (Italy), on an external OpenStack infrastructure. We start from presenting the experience on a first work on the "Cloud Bursting" of a CMS Grid site using a novel LSF configuration to dynamically register new worker nodes. Then, we move to an even more recent work on a "Cloud Site as-aService" prototype, based on a more direct access/integration of OpenStack resources into the CMS workload management system. Results with real CMS workflows and future plans are also presented and discussed.