We investigate the possibilities and limitations for the development of new electronic density functionals through large-scale fitting to databases of binding energies obtained experimentally or through high-quality calculations. We show that databases with up to a few hundred entries allow for up to of the order ten parameters to be adjusted in the exchange enhancement factor. The transferability of models between data is analyzed, and it is shown to be difficult to transfer a model trained exclusively on molecular atomization energies to the treatment of chemisorption systems.