Enhancing an existing warp drive system is possible, both in space and in a dry dock facility.
Without restructuring an existing ship some warp power increase is possible (computer controlled field output, limited plasma delivery alterations, etc..) but a real increase in efficiency and power requires time at a dry-dock facility where the warp drive components are physically modified and adjusted to increase power output. New field coils, specialized plasma injectors, restructuring of the reaction chamber, or the matter/antimatter injectors themselves... It is analogous to the fact that a person can only improve combustion engine performance to a point simply by adjusting how the onboard computer manages the engine, fuel injection, and transmission.
Adjusting Warp Field Geometry
This method essentially adjusts the shape, size, and varies the field strength at various stress points along the field to active greater efficiency when translating warp power to actual ship movement. Some of this can be done with a computer program, but that is limited. For a substantial increase in warp speed the field coils must be modified in shape, size, orientation, and plasma injection orientation / size of injection stream.
Adjusting Warp Core Performance
This method provides a higher quality plasma output from the warp core to the field coils. Giving a higher efficiency transfer of plasma energy to the warp field, thus moving the ship faster. This method also allows for more power output to other systems as well.
Changing Delivery of Warp Plasma to Field Coils
Warp plasma, like any energy source, looses power on the way to its destination. If delivery can be adjusted to provide higher efficiency of power transfer to the warp coils themselves, efficiency (and in turn speed) can increase.
Preventing Component Burnout
The amount of physical room high capacity components take up inside a ship design combined with the amount of weight those components add to a ship for the purposes of moving the mass through space (and adjusting a ship's mass via a Warp Field for propulsion) limits the speed of a vessel of any particular size, but especially smaller ships with very limited space. This is crucial when modifying an existing space frame to increase speed. Thus, preventing burnout of existing components is critical to increasing speed. If drive components can have more energy of higher power delivered to them without burning them out speed and efficiency increase without the need for higher capacity components.
An Importan Note
Modifications of any kind past the standard operating specs can be dangerous, failures both minor and catastrophic are a distinct possibility when pushing a ship beyond it's designed safety limits.
For instance... When increasing the speed of a warp drive system the stress to the space frame is also increased, this must be accounted for. A small failure during normal operation can snowball quickly into a catastrophic failure after modifications are applied.