Having an end sound produced in a unique environment that is being identified as not able to produce an impression that has an appeal can be the result of more than a Xover design and accusation the Xover design needs improvement.
A Speaker is typically designed in a very disciplined manner and in conjunction with control measures, where the ambient space the Speaker is used in during the design stages through to final design is quite different from a ambient space a Purchased Speaker will reside in while used.
Every Speaker Produced and Sold from a particular model, is to become a Speaker that has its own unique interpretation of its end sound produced. Each unique space the speaker is set up in for its period of residence, will have its own unique voicing for the end sound. The energies produced by the Drivers and sent in to the Ambient Space is going to produce a unique sound scape within each space the Drivers and Cabinet are used in.
The source of a sound heard should not be detectable, and that is not suggesting it is only the Speakers Form and placement in the space that should not be identifiable. Energy Transferred as Sound can have pin point locations identified where it is reflected from or unsettles the structures within the room.
Xover design is not going to remove certain frequencies that are not being managed well within the room, unless the Xover is a design that removes those frequencies from the Frequency Range of the Speaker.
The Space selected for the Speaker and the Speaker within the selected space, needs to be worked with to find something that represents a optimised interface / coupling to each other.
Coupling a Speaker to a room is the way forward to create a confidence the speaker interacts at its best when transmitting sound through the physical structure of the room, including the floor, walls, ceiling and locally placed items.
The Speaker / Room Interaction can have a profound effect that is a negative impact on the quality of the sound being transferred. Creating effects like room modes (standing waves), Reflected Sound, Causing Local Placed Materials to produce sound. Each when being generated will be negatively affecting the overall acoustic characteristics of the room.
Xovers design does not do anything to alleviate the above influences on produced sound.
The good news being that putting measures in place to tidy up the Speakers Coupling to the Room are not necessarily expensive, bit do need a little creativity if the decor and aesthetic for the Space supplied for the Speaker is to be maintained to a particular appeal. An acoustic fabric might need to be dyed to color match a wall color. An Absorption Panel, may have a dimension that matches a Wall Art Picture that can then be mounted on to the absorption panel. Diffusers are able to be found that look like a Sculpture and be a feature in a room, or a cheaper version is able to be sourced / produced that again can be blended to the room color or concealed behind a fabric.
Where the interesting area is to be found is the impact of the siting within the room for such ancillaries to assist with managing energy transfer into the Space.