No room for a new "_thing_"
The technology available to Knuth at the time TeX was written is said to have been particularly poor at managing dynamic storage; as a result much of the storage used within TeX is allocated as fixed arrays, in the reference implementations. Many of these fixed arrays are expandable in modern TeX implementations, but size of the arrays of “registers” is written into the specification as being 256 (usually); this number may not be changed if you still wish to call the result TeX (see testing TeX implementations).
If you fill up one of these register arrays, you get a TeX error message saying
! No room for a new \<thing>.
\things in question may be
\count (the object underlying
\skip (the object underlying
\box (the object underlying
\newsavebox command), or
\language (all types of object
whose use is “hidden” in LaTeX.
Originally the the limit on the number of these registers was 256
\write objects, just 16. Current LaTeX formats
are always built with $\epsilon$-TeX extensions
enabled, which means that there are 32768 registers available for the types
\write. LuaLaTeX extends this further with 65536
registers for most types, 256
\write streams but still 16
Most commonly if you get this error now for types other than the file streams it is because you have an old (pre-2015) LaTeX format which is checking the original limit of 256, even if an extended TeX is being used. Updating to a current LaTeX release should fix the issue. If you have really used up 32768 registers then most likely you have a programming error that is causing a loop to allocate all available registers and so an enlarged TeX would not help. You could however, try with LuaLaTeX which has larger limits in most cases.
One related error is an error that the number of
\inserts has been exceeded.
An insert is not a register type but requires allcation of matching count, skip
dimen registers with the same number, in all current engines there can be at most 256
inserts. You are unlikely to get this error on a LaTeX format newer than 2015, however
if you have to use an old format the Morefloats package
is available that increased the number of inserts available to the float mechanism.
The number of write streams is limited to 16 (or 256 for LuaTeX) even with extended TeX, however the
morewrites package can provide the illusion of large
Source: No room for a new "_thing_"