Just to cover part: Never simply "oblige the request". That's bad for everyone. I always let a client tell me what they THIINK they need to rank for and how. Then we explain with data why that should or should not be part of the strategy.
We have clients that make recommendations for changes they want and they understand that if we say "it's because of SEO". They will back off and let us maintain the process.
Partial SEO would be, a home page optimization? That's fine as long as long as you verify and understand the scope of the rest of the site. Nothing wrong with "doing a little work" on your highest possible ranking piece of real estate. In the end, it's all in the reporting and measurement. You just have to be able to communicate whhat you are actually going to deliver.
Hope this helps a bit.