Are there bodies of water similar to the Dead Sea, where someone can float without having to move?
Yes, there are other highly saline lakes and "seas" similar to the Dead Sea.
Wikipedia maintains several nice lists with examples:
a list of salt lakes
Even the list of drying lakes many of which experience their salinity increasing, some even beyond the average salinity found in the Dead Sea (which is what allows most people to remain naturally buoyant there).
Including among others:
the Aral Sea; "by 1990 it's salinity was at 376 g/L. (By comparison, seawater is typically 35 g/L, and the Dead Sea between 300 and 350 g/L.)"
Lake Retba where "salinity can reach as high as 350 g/L during the dry season".
From before the question was edited:
Is there any other well known water body like the Dead Sea? Where a person does not drown?
As Willeke and others already commented and implied: the high salinity in the Dead Sea increases the natural buoyancy of people, but the fact that most people won't sink, doesn't mean that people will/can not drown there. Lie face down for long enough and you will of course still drown.
Many assume that it is impossible to drown in the Dead Sea due to its high salt content, which stops swimmers from sinking and enables them to float on its surface.
However, the very buoyancy that attracts visitors can turn deadly if a swimmer flips over onto their stomach, because it is difficult to force the feet down to turn back over.
Wikipedia has already done most of the work for the question you probably intended to ask "are there other lakes like the Dead Sea with very high salt content?"