This is an interesting question. A general rule in cryptography is that creating any patterns in keys or passwords is a bad idea, because patterns weaken the system. For example in your case say you log into 10 websites using a base password of myb@s5PW, and add a password suffix on the end. Maybe for stack exchange you use myb@s5PWstEX, for blog site a you use mhb@s5PWblSI, etc. Or maybe you use aamyb@s5PW and bbmyb@s5PW instead. Either there is a discernible pattern, even if there's only one password known.
Let us say that Stack Exchange was hacked (unknown zero day vulnerability, nothing they could do about it), and all user passwords were gained, including yours. I'm sure that somewhere someone is putting this information into a database, so that DB will then have your username with a password next to it. Say then the blog site was hacked the same way, then there would be two passwords linked to your username with an easily understood pattern. If someone wanted to hack one of your other accounts all they'd have to do is make educated guesses based on the pattern. You could make this more difficult by making your patterns more complex, but it's so easy to brute-force all combinations of myb@s5PW that no amount of complexity isn't going to make that strong. If fact it wouldn't be a stretch for an attacker to figure out your pattern even with one example, if they were looking for it that is, but it's unlikely one would try unless they were targeting you specifically.
So from a pure code-breaking perspective it's a bad idea, but like so many other things in security that's not the only factor. The fact is that most people use the same password for multiple sites with no variation at all, so a hacker who gains the password for one site will in many cases get access to loads of other sites. Why would a hacker go through the trouble of looking for patterns when they potentially have millions of user accounts to tap with no work whatsoever? Only if they are targeting you specifically would you need to worry about that.
Add to that the issue of remembering multiple complex passwords. Unless you are Rain Man you would never be able to memorize 40 strong passwords, so having a base password system that makes sense to you but would take some work to figure out is a workable solution for today's authentication issues.
As as for keeping them all straight write them down, and keep them in a locked desk at work or in a locked drawer in your home. Seriously, the vast majority of people who are trying to gain your passwords are probably halfway across the world from you, who is going to break into your home or work to gain the passwords to your stack exchange account!
This is an approach based on someone with an average level of risk. If you do know someone who might break into your home in order to gain your passwords then using any sort of pattern in your passwords is a bad idea.