For example, if you personally knew a slaver, could you arrange a deal on an individual basis -- like, "can you get me such-and-such type of slave?" I ask because some characters in one of my stories meet with a slaver under the pretext of an private business negotiation and trick him into confessing to illegal business practices.
In fact, his sort of transaction happened more than you would think!
Livy records in his book Urbe Condita Libri (The Book on the History of Rome ) How the slave market varied all over the Empire depending on the different needs and the different cultures that the Empire was home too.
Livy notes that although most of the slave-trading took place in open market squares that were reserved for such business. People oftentimes made "deals" with the slavers to get a specific type of slave for a specific job.
While the rudimentary house slave can be bought relatively cheaply at the market, the owners of these Gladiotorial schools often preffered soldiers. Men already trained in combat. This meant that they could profit of their investments much more earlier as training men in the art of combat takes time -Livy
Here Livy illustrates an example of this paradigm. Gladiatorial Master's wanted soldiers as slaves and they were ready to pay a handsome amount for them and thus the slavers delivered. You see a deal like this struck profit for both parties involved. The Gladiator Masters got the choicest of slaves and the slavers were able to sell them up to 2x the normal price.
In his Journal article, "The Early Development of Slavery in Ancient Rome" Keith R. Bradley also points out how a similar phenomenon would take place where rich men would often pay twice the price and even carry out favours for slave girls whom they bought to be their mistresses or serve as prostitutes in their brothels.
Lastly, you do have to remember the Slaves in all sense were a commodity in Ancient Rome. They were used as a method of transaction in many cases (As both Tacitus and Livy have recorded). Rich people bought them as gifts for their friends (Much like they would buy Dogs) and people would generally be willing to do favours and pay more for their personal choice of slaves (i.e that the slavers deliver to them first)
Every Slave was different and thus were rarely interchangeable. Some Slaves were a very close part of the household. Others were treated worse than Dogs. The type of men/women fulfilling each of these roles was also different and thus if you wanted a certain type of salve for a certain job, you could definitely ask!
Do note that the Poor Man's slaves often worked hard construction projects and thus were often times bought in very large quantities by the Senate.
Sources
https://www.jstor.org/stable/41298844?seq=1
-Paper by Keith R. Bradely on the Slavery in Ancient Rome
https://en.wikipedia.org/wiki/Ab_Urbe_Condita_Libri
-The Book on the History of Rome by Livy
https://www.amazon.com/Annals-Imperial-Rome-Cornelius-Tacitus/dp/1420926683
-The Annals of Imperial Rome by Tacitus
-History of the Decline and Fall of the Roman Empire [Volume IV] [Chapter XXVI] by Edward Gibbons
-Study by Dartmouth University on how Slaves were an integral backbone of the Roman Economy. T
https://www.jstor.org/stable/651186?seq=1
Novel Evidence for Roman Slavery
-Paper by Keith Hopkins
http://classics.mit.edu/Antoninus/meditations.html
-Meditations by Marcus Aurelius
^(Note: Marcus explores a bit of the philosophical side of slavery. He questions the morals behind slavery but before that, he does illustrate the different practices of slavery which were common in the Empire. A bit towards Philosophy but an excellent read nonetheless!)