Numerous components used in experimental and actual devices, processing the light or electromagnetic fields in the nanoscale, have a wedge shape. Since increased power concentration is always desirable in optical signals and field distributions, it is worth trying to enhance the electrostatic intensity in the vicinity of those wedges. In this work, such a purpose is served by another wedge, an auxiliary dielectric nanotip, posed 'nose-to-nose' with the primary metamaterial wedge to form an asymmetric 'bowtie' configuration. We define a quality factor expressing how amplified is the field into the primary wedge compared to the case that the secondary component is absent. This quantity is represented with respect to the parameters of the nanotip (permittivity, angular extent) and significant peaks, corresponding to maximum power into the primary component, are observed and discussed.