I have a site that is ranking bottom of page 1 for "IT support company" - however, I have since realised there are other keywords I could be ranking for as well, such as "IT support services," had I started off with a more long-tail keyword such as "IT support services company."
This is where planning and evaluating needs to take place.
You say you're ranking at the bottom for "IT support company". I'm assuming that's your title. Remember, the rank is mostly based on your title, meta description, words in H1 and H2 tags, and especially the queries people use.
What you should do is register your domain with Google Webmaster Tools and go to the search analytics section. In their older interface, there will be several columns.
One column lists the words people search, another column lists impressions, and another lists clicks as well as average search position.
Impressions means visitors saw your webpage in the search results when they searched for that specific term. clicks mean they accessed your site by clicking a search result.
If you want to rank high, look for search terms with a very high impression count and a very low click count. Next, try to adjust your title and meta description of your site to include the terms in exact order if possible.
So if you see in analytics that theres a high impression count for "IT services" and hardly any clicks for it, then change your title so the words "IT services" are included. If you want the word support added, then change it to "IT services plus support" or something like that.
My question is, what results has anyone seen who has ever tinkered with a well-ranking page to try to add in another keyword?
I tinker with keywords as often as necessary and when I change my keywords to common words people use more often, I get more clicks into my page.
I'm nervous that if I make any changes to the page title, for example, then I might drop for the first keyword and never recover! Or would restoring things if that happened eventually cause it to recover?
If you select a title that does not make sense or you select a title that doesn't fit with the content of your page, then expect rankings to drop. I can't see reverting back to the old title help you much. Your best friend is Google Webmaster Tools search analytics section. It can tell you what people search for in a time period and you can change that time period to understand search trends in relation to your site. It may be possible that in the last three days no one wanted to search for IT services or support.