It depends of what kind of "SEO". Some elements of SEO have to be taken in consideration before or during the development of the site and should be on the todo list.

Secondly what are the first steps one needs to take in optimizing an existing website, one that an extensive SEO Work has been done on previously,

Review what was done,
Check if this was done correctly,
Check if optimizations are still up to date,
Remove useless things,
Add your own optimizations,

Start the the content. After all content is king.

Make sure the leads/crawl are accurate.

The rest will take care of itself.

If you want to game (seo) you can do that at anytime. After all, SEO is making a square peg fit a round hole (it will, but the square has be be a lot smaller than the hole... and about as useful).

Or, code for content, the USER, and the search engine will place it properly. These days SEO actually means don't do something stupid.

3) Before you even begin building anything.

When is the best time to start an SEO process for a site

Yesterday.

I am 100% sure that SEO is better to start practicing before starting to develop a site. I worked with clients who couldn't do SEO. They needed to change the site again, which is much more difficult than everything to foresee.

Yes it is best to build a website after having an SEO strategy with proper keyword research, established content to write, and planned structure for how the website maximizes user experience etc.

SEO strategy should not be an afterthought, it should a core part of the website creation.

I've been working with many web developers from that past and I always recommend to them to create a "Launching Landing Page". This page will be used to display the date and time the website will be up and live.
The launching page will be indexed but should only contain few information.
The ultimate reason why we need the homepage (launching page) to be indexed in an early stage of development is that Google will be able to record and indexed the page thus contributing to "domain age".
Domain age is a crucial part of SEO since Google favors websites that are present on the web for quite sometime. Being present on the web increases your reputation on search engines and builds trust. Since your showing that you are not a fly by night kind of site.

Just after the idea epiphany, and before buying the domain name.
:-)

I feel that, if at all possible, SEO should be considered before the business plan has been formulated.

Its depend with your current condition. If you want to starting SEO strategies, you can start immediately and simoultant with your developer to finished the design.

The sooner you start SEO, the sooner you will start to see your rankings improve.
If you are changing domains or starting on a new domain, wait to begin SEO.
Things to Optimize Before Your Site Launch
Using Keywords in URLs
Responsive Web Design
Optimize your Visuals
Link Structures that Crawl

Hi,
The best time to start an SEO process is just after buying your domain name. After having a domain name you can start with branding and after completion of website structure you can start On-page SEO, you can focus on your keywords can optimize content as per your keywords. After completion of On-page SEO, you can focus on Off-page SEO with quality backlinks which will help you in ranking your keywords in SERP.

I always started my SEO aims at the start of the project to produce the site, it is critical when developing content - and when deciding on structure of pages and directories. I think keyword research begins before those two also..

Yesterday.

This.

Even if I often criticize "SEO", you need to think about everything at first, and keep these in mind when you develop your project. If you say, oh, I'll look at this later, then you might end to have to redo a lot of work later. So try to figure all aspects at first, how to achieve then, then start developing your project, and also keep these goals in mind.