Yes. There are examples of slaves owning slaves from different historical periods and in different regions of the world, including:
- Ancient Near East
- Early Medieval Sunni Islam
- Late Medieval Mallorca
- 19th century Brazil and the West Indies
- Pre-colonial and colonial East and West Africa
Ancient Near East
In the Neo-Babylonian period (605–333 BC),
there is a wealth of documentation about slaves, working in three
capacities. First, there was a small number of royal slaves....Then
there were slaves as janitors owned by the temples...Finally, the
largest and best-known group of slaves were those owned by private
persons. Among them we see great variety in the tasks performed, from
agriculture to loan-sharking.
...The loan-sharking slaves could become very rich and in some ways quite
powerful. They could marry in legally recognised weddings and must
have known the high and mighty who gave them loans. They probably had
access to amenities that very few free Babylonians could afford, and
many apparently invested for themselves on the side and so controlled
their own money as a peculium. They also owned their own slaves. But
they never were allowed to accumulate enough money to buy their
freedom or the freedom of their loved ones.
Source: K. Bradley & P. Cartledge (eds), The Cambridge World History of Slavery, Vol 1: The Ancient Mediterranean World, p.15
M. A. Dandamaev's key work Slavery in Babylonia: From Nabopolassar to Alexander the Great (626-331 B.C.) states that slaves also owned slaves (and land) during the (earlier) Neo-Assyrian period (911 - 609 BC).
Medieval Sunni Islam
Kecia Ali, in Marriage and Slavery in Early Islam (Harvard University press, 2010), under a sub-heading 'Slaves Owning Slaves', writes that in Maliki doctrine,
The Mudawwana considers, for example, a case where a free man swore
that all his slaves (mamdlik) were manumitted "and he [the free man]
has slaves and his slaves have slaves." In such a case, according to
Malik "only his [i.e., the free man's] slaves are manumitted and his
slaves' slaves are left in the possession of those of his slaves whom
he had manumitted, [remaining] enslaved to them ." Given that
slaves could own other slaves, Malik granted a male slave licit
sexual access to his female slaves, subject to the same restrictions
as a free owner.
Late Medieval Mallorca
In late medieval Mallorca, after it had been taken from the Moors by James I of Aragon,
there is scattered evidence of Mallorcan freedpersons and slaves
owning slaves. In 1337, the Greek Serena, from the village of Muro,
unconditionally manumitted her slave Antonia. At the end of the
century, the slave Catalina petitioned for back pay owed to her slave
Antonio. The practice continued into the fifteenth century, as when
the freed Circassian slave Margarita manumitted the four month - old
daughter of her Bulgar slave in 1404.
Source: Kevin D. Mummey, 'Women, Slavery, and Community on the Island of Mallorca, ca. 1360-1390' (Ph.D thesis, 2013)
Slaves also owned slaves in the West Indies. James Rodway, in The West Indies and the Spanish Main (1899), contrasted the difference between slaves of rich planters and those owned by poor white men and other slaves.
the miserable, broken-down creatures sold cheap as refuse lots to poor
white men or even to slaves. Yes, the slaves bought their diseased
fellow-countrymen, to work on their own allotments, treating them as
the costermonger sometimes does his donkey. Half-starved, hard-worked,
and covered with sores, they lingered in misery until death came to
make them free. Some were so disfigured with yaws, or leprosy, that
none but a negro could bear the sight of them; these were kept out of
the way and treated worse than mangy dogs.
19th Century Brazil
Mieko Nishida, in Slavery and Identity: Ethnicity, Gender, and Race in Salvador, Brazil, 1808-1888 (Indiana University Press, 2003) refers to "slaves owned slaves":
ex-slaves or sometimes even slaves themselves, who did own any other
form of property owned slaves.
Pre-colonial and colonial East and West Africa
This is very well documented, partly due to the involvement of Dr. Daniel O’Sullivan-Beare, the Vice Consul on Pemba Island in 1895. One early case was that of Mzuri Kwao:
Mzuri Kwao became a mtumwa ya mtumwa, a slave of a slave. This is a
term that is rarely discussed in the literature on enslavement along
the coast. Yet it comes up several times in the documentation of
slavery on Pemba. Being the slave of a slave meant that the
slaveholders had little benefit to offer slaves in terms of social
status or even security. If slaveholders were enslaved themselves,
they could not guarantee where their own slaves could live, whether
they would be resold, and who would inherit them at the death of their
owner, among other problems. However, the ownership of slaves by other
slaves indicates the ability of slaves to own property even before the
British Abolition Decree.
Source: Elisabeth McMahon, 'Slavery and Emancipation in Islamic East Africa' (Cambridge University Press, 2013)
In a footnote, McMahon gives further information and references on slaves owning slaves, also mentioning West Africa
Prestholdt discussed the concept of slaves owning slaves as a means to
remake their status in the society. Jeremy Prestholdt, Domesticating
the World: African Consumerism and the Genealogies of Globalization
(Berkeley: University of California Press, 2008), pp. 134–40. Abdul
Sheriff mentions this in passing for mid–nineteenth century Zanzibar
Town. Sheriff, 1987, p. 149. Klein notes in passing that is was a
common system in West Africa; rather than slaves buying their
emancipation, they bought their own slaves because it gave them more
security in old age. Klein, 1998, p. 13.
On slave hierarchy, McMahon's book contains a clear example in East Africa:
Within the social world of slaves there existed a hierarchy based on
gender, occupation, and the process of enslavement. Slaves of equal
social status referred to each other as njoli. Thus vibarua would
describe each other as njoli, but a kibarua would not call a mtumwa ya
nyumba a njoli because their positions were not socially equal.
Vibarua usually lived in urban centers independent of their owners.
They paid a daily or monthly wage to their owners, wherein mtumwa ya
nyumba mostly lived in rural areas doing hard agricultural labor under
the oversight of owners or overseers.
Slave hierarchies were in fact widespread; for further examples, have a look at The Diversity of Private Slaving Strategies in Classical Athens and (for Imperial Rome) Slaves of Slaves: The Complex Status of Imperial Vicarii.
(all emphasis is mine)