After removing w3tc, have you use the command
ee site update yoursite.ltd --wp ?
Because EasyEngine set custom nginx configuration for each cache mechanism, and --w3tc include nginx directives which may not work properly with another plugin.
Additionally you have the choice with several other cache mechanism :
ee site create example.com --wpsc # install wordpress with whisp-super-cache plugin
ee site create example.com --wpfc # install wordpress + nginx fastcgi_cache
ee site create example.com --wpredis # install wordpress + nginx redis_cache
But to answer to your question about WP Multisite, you can convert your current wp instance in a multisite with the command
ee site update.
The documentation page is available here : https://easyengine.io/docs/commands/site/update/
Before trying a command, make sure to backup your wordpress files and your database.