Naive question: Is it possible to somehow download GLIBC 2.15, put it in any folder (e.g. /tmp/myglibc) and then point to this path ONLY when executing something that needs this specific version of glibc?

Yes, it's possible.

To install glibc 2.14 in parallel, add the configure prefix:

tar zxvf glibc-2.14.tar.gz
cd glibc-2.14
mkdir build
cd build
../configure --prefix=/opt/glibc-2.14
make -j4
make install

Following this process, you'll be able to build 2.14 but you will need to tell the compiler where to look for glibc.

Below are the ways you can expose the glibc to your program.

1. LD_LIBRARY_PATH=/opt/glibc-2.14/lib

   export LD_LIBRARY_PATH.

   The library is exposed during your current login session.

2. You can permanently link your new glibc version like so, but please read the WARNING below:

   ln -sf /opt/glibc-2.14/glibc-2.14.so /lib/libc.so.6.

Since libc.so.6 is just a symbolic link. Executing the above command will make the link point towards the new glibc library. However this step is not recommended since there are many programs in Linux which depend on older versions and will stop working.

I found this source very useful and doesn't has much SEO. It lists the most common errors you might encounter while using @UnitasBrooks great answer and I'm afraid it gets lost in the future.

This is the link to the original post

I will copy, paste it here (I faced the last problem and it fixed it, however I didn't try all the problems/solutions listed and you try it on your own risk)

Glibc installation

The GNU C Library, commonly known as glibc, is the GNU Project's implementation of the C standard library. My environment required glibc (version 2.14) and it took a bit of fiddling to get it to work, so hopefully this will save you some time.

0.Glibc Installation Dependencies

Bash: sh
Binutils: ar, as, ld, ranlib, readelf
Diffutils: cmp
Fileutils: chmod, cp, install, ln, mknod, mv, mkdir, rm, touch
Gcc: cc, cc1, collect2, cpp, gcc
Grep: egrep, grep
Gzip: gzip
Make: make
Gawk: gawk
Sed: sed
Sh-utils: date, expr, hostname, pwd, uname
Texinfo: install-info, makeinfo
Textutils: cat, cut, sort, tr

1.Download installation package

http://www.gnu.org/software/libc/ for all versions.
http://ftp.gnu.org/gnu/glibc/glibc-2.14.tar.gz for version 2.14.

2.Compile and install

To avoid disturb current environment, compile and install this version separately by configuring prefix.

[root@localhost ~]# tar xvf glibc-2.14.tar.gz
[root@localhost ~]# cd glibc-2.14
[root@localhost glibc-2.14]# mkdir build
[root@localhost glibc-2.14]# cd ./build
[root@localhost build]# ../configure --prefix=/opt/glibc-2.14
[root@localhost build]# make -j4
[root@localhost build]# make install
[root@localhost build]# export LD_LIBRARY_PATH=/opt/glibc-2.14/lib:$LD_LIBRARY_PATH

3.To check glibc versions installed

root@localhost:~/intel64/runtime/glibc$ strings libc.so.6 | grep GLIBC
GLIBC_2.2.5
GLIBC_2.2.6
GLIBC_2.3
GLIBC_2.3.2
GLIBC_2.3.3
GLIBC_2.3.4
GLIBC_PRIVATE

4.Compiling errors

Error:

make[1]: *** No rule to make target /mnt/lfs/sourcenew/glibc-build/Versions.all', needed by/mnt/lfs/sourcenew/glibc-build/abi-versions.h'. Stop.

Solution:

sudo apt-get install gawk
sudo apt-get install texinfo

Error:

make[2]: *** [/mnt/lfs/sources/glibc-build/misc/syslog.o] Error 1

Solution:

make clean
make -j2 CFLAGS="-U_FORTIFY_SOURCE -O2 -fno-stack-protector"

Error:

/Downloads/glibc-2.14/build/elf/ldconfig: Can't open configuration file /opt/glibc-2.14/etc/ld.so.conf: No such file or directory

Solution:

:/opt/glibc-2.14/etc$ sudo sh -c "echo '/usr/local/lib' >> ld.so.conf" 
:/opt/glibc-2.14/etc$ sudo sh -c "echo '/opt/lib' >> ld.so.conf"