@traudio I feel a good place to start is not to steer you away from your current set up in a direction that comes with considerable cost.
Firstly your V10 has a range of Capacitance Settings to be used with the Mk III Cart', 47-367pf to be reasonably accurate.
Making adjustments across this range of settings will have an effect on the Mid's to High Frequencies.
If the V10 is with default setting the Mid and High frequencies are most likely most prominent, as soft furnishings will absorb these, so avoiding the any concerns voiced about sounding 'rolled off' are calculated for using the default.
The coherence across the frequencies can be attempted to be addressed by using the Cap' Adjustment, there is a possibility the Bass may come forward as having a little more prominence.
The area I am unfamiliar with is that in general as a description the V10 is suggested as being revealing and insightful, such traits would suggest a very honest bass note with a well defined decay (transparency). Such traits will be difficult to describe as having a tone that leans toward being warm.
So far no costs are to be incurred.
If Cap' Adjustment does give the Bass a increment of being present in a more perceivable way, there are methods to add a little Richness in Tone.
One method experienced across a variety of systems in the homes of other audio systems is the use of a Cable that has D.U.C.C wire as the signal path. This wire has been proven in use to remove nothing that is recognised and valued in a recording, it delivers with a slightest of underpinning to the Vocal and Notes, which can be referred to as a Hint of Richness. This might be the level of transition from transparent to rich that is to your satisfaction.
I would suggest these in use, at the shortest length usable, as TA >Phonostage and then swap as Phono'> Pre-Amp'. If something is found to be if an attraction in both placements, I suggest buying in a second pair and Cart' Tag Wire using the same wire.
A careful hunt could get all cables, 'if wanted', acquired for approx' £200
Additionally, another method used, but from my experiences had, not proven to be ubiquitous, is the use of Platter Mats.
I have many in a variety of materials, to date I have found Ceramic and Forex Foam to be very noticeable for adding a perception of a Rich Tone, with 5mm Thick Forex Foam being the most noticeable, it has real attraction, as it does not remove any valuable info being extracted from the recording. It has proven in use to be more attractive than the same material in a 3mm thickness.
Forex is very cheap, I acquired mine for approx' £5 per mat, I have gifted this material to other BD TT users who have been thoroughly impressed during their demo's received.
I feel confident based on previous experiences that the use of a Forex Foam in conjunction with the option to Cap' Adjust will bring a eyebrow raise, even a big smile.
Cables can remain as a curiosity and intended luxurious purchase, leaving the investigation being suggested a very inexpensive pursuit.