Installing Python manually is possible. As an example, you can use the following instructions to install 3.5.2 version

Prerequisites

Install dependencies :

sudo apt-get update && sudo apt-get install libssl-dev openssl

Building Python

You can build Python in a specific folder using the --prefix parameter from configure command:

wget https://www.python.org/ftp/python/3.5.2/Python-3.5.2.tgz
tar zxf Python-3.5.2.tgz
cd Python-3.5.2/
./configure --prefix=/usr/local
make
sudo make install

Instead of /usr/local, one can use another base directory. As an example:

sudo mkdir /opt/python-3.5.2
./configure --prefix=/opt/python-3.5.2

Selecting python version

Using PATH environment variable can help choosing the right python version to use. But one can also use symlinks:

sudo ln -s /opt/python-3.5.2/bin/python3.5 /usr/local/bin/python3
sudo ln -s /opt/python-3.5.2/bin/pip3.5 /usr/local/bin/pip3

Using -f option will allow you to replace existing symlinks