Because you cannot use the same SSH key for multiple accounts on Github, Gitlab, Bitbucket, etc, you will need to generate multiple public/private keys and use them accordingly.
Let's create a ssh key
ssh-keygen -t rsa -C "user-1@example.com"
You will be prompted for an optional password. It depends on you if you want to have a password or not for this.
Copy the public key (Mac OS)
pbcopy < ~/.ssh/id_rsa.pub
And paste it in your git server account SSH keys page. You may see here how
If you use only one account, then you can stop here.
Generate a new SSH key with a different name
ssh-keygen -t rsa -f ~/.ssh/second-account -C "user-2@example.com"
Now, you need to create the file ~/.ssh/config
with the following content:
Host bitbucket.org
User git
Hostname bitbucket.org
PreferredAuthentications publickey
IdentityFile ~/.ssh/id_rsa
Host bitbucket-second
User git
Hostname bitbucket.org
PreferredAuthentications publickey
IdentitiesOnly yes
IdentityFile ~/.ssh/second-account
Now, to use the primary ssh key to clone a project you use the following command
git clone git@bitbucket.org:username/project-name.git
And for the second account you'll have to change the hostname in the url like this:
git clone git@bitbucket-second:username/project-name.git
The example was provided with an example to bitbucket, but in the same way it works for Gitlab, Github and any other git servers.