For two main reasons besides the obvious necessity to perform the most precise characterization of the new particle.  Firstly, we want to understand how the physical vacuum in which we live was created in the early universe.  Secondly, we want to understand which this physical vacuum can be made stable.
The Higgs field is very unique as it provides a non-zero mean expected potential energy to the physical vacuum! This is, fundamentally, what makes the whole difference for our universe. We believe that it is possible to access the shape of the energy potential which is responsible for the electroweak symmetry breaking, that is of the very existence of the electromagnetic force of infinite range and of the weak force acting at very short ranges. It turns out that to do this, we have to study the way the Higgs bosons interact with themselves! And for this, we need to produce pairs of Higgs bosons!
The Higgs boson solved the question of the origin of the mass of all other elementary particles, but its own mass is unexplained. This mass is not protected by any symmetry of the theory, and it brings unwanted instability in the theory.  So much, so that via quantum processes, the physical vacuum itself could become destabilized by quantum fluctuations. Fortunately, this is on timescales considerably larger than the known lifetime of our universe, but we are nevertheless looking for additional Higgs boson-like particles that would signal the existence of the new physics needed to stabilize the Higgs boson mass.
All this motivates the analysis of much more data and, if possible, access to higher collider energies. This is why thousands of scientists from all around the world are still dedicated to the task!