Here's a quick summary:
Suppose you donate $100 to SCI. By doing so, you're saying that SCI is the best use of $100. Now suppose you donate another $100 to AMF instead. By doing this, you're saying that AMF is a better charity to donate to. This can only be true if your past donation to SCI was a mistake (and therefore you should have given all $200 to SCI) or the $100 you gave to SCI fulfilled all their need for funding.
But SCI has lots of room for more funding, so unless you're donating millions of dollars, you're unlikely to have changed which charity was the best. So either your second donation should have gone to SCI, or the first should have gone to AMF. Either way, all your money should be going to the same place.
There might be some good reasons to donate to multiple charities, for example if you're a millionaire and can overwhelm an organization's room for more funding, or if you get new information and change your mind on which organization is the best. But there also are some reasons that aren't up to snuff.
True, our knowledge is never 100%, but we have to choose somehow. Your donation to AMF simply means that, given what you know, taking into account our credences for different outcomes, to the best of our judgement, as far as we can tell, AMF is the most cost-effective charity for your first $100. And that means it's probably still the best charity (as far as our evidence shows, in our best judgement, as far as we can tell) for your second $100.
If you have two charities, one is going to be a better place for your money than the other. If you split between them, you have a 100% chance of picking the winner, but you also have an 100% chance of picking the loser. Think of it like two lottery tickets - one that wins 60% of the time and one that wins 50% of the time. While it's true that the first ticket might lose and the second one might win, it's less likely. Therefore you should put your money only into the first ticket. Likewise, you should only put your money into the charity you think has the highest chance of being best.
It is important that we try many different approaches to solving poverty, hunger, and other global problems. After all, some might fail while others work better than expected - by having a variety of charities, we reduce our risk. Because of this, you should take into account how much each charity aids the global diversification effort when judging its effectiveness, and give all your donation to the charity you think is currently most underfunded. Because it's the charities we want to be diversified, rather than your individual donations, the argument still applies: give all your 10% to the best charity - which might be best because it contributes most to the diversification of the global charity portfolio.
We diversify our financial portfolios because we care about the risk to ourselves, not just to the global economic system. With charities, we instead fundamentally care about the people we're helping, and reducing the risk to them. Donating to just one charity might increase the risk that my donation is less effective but reduce the risk to the beneficiary, it insured them against a tail risk. As we are donating to help people, rather than for self-gratification, this is a worthwhile tradeoff.
Alternatively, think about the size of your efforts compared to the overall problem. With your portfolio, you buy Google or Microsoft to work on the 'not having any tech stocks in your portfolio' problem. You buy enough stock to completely solve the 'being underexposed to tech' problem - so the rest of your investment can go into other stocks. With AMF, however, your donation is unlikely to solve the 'SCI doesn't have enough funding' problem - so further donations should still go to SCI.
You might think this means we should always donate to small charities, because donations make more difference to them. But the important thing isn't the percentage increase in charity revenues, but how much good the extra funding does; if a big charity is more cost-effective than small ones, we should donate to the big one. Larger charities might have more trouble with fungibility though.
If you really liked a certain charity, presumably that means you believe in its mission and want that mission to succeed. But if you believe in its mission, you should want to donate to a charity not because you want to be nice to the charity, but because you want the mission to be accomplished. Therefore, you should give to whatever one organization you think best accomplishes that mission.
This wouldn't happen because it's impossible to get everyone to coordinate that well. Secondly, even if everyone in the world were on board with Giving What We Can, people would still take into account room for more funding. A general strategy of "everyone donates to the charity that does the most good" would lead to different people donating to different charities; people would donate to SCI until it no longer had room for more funding, and then the next people would donate to AMF until it no longer had room for more funding, then the next people to Deworm the World, and so on.
Yes, we have many different values. But at any given time, one of these will be the most pressing; one of them will be easiest to make headway on. And that's the one we should concentrate on. By focusing all our resources on one cause, we have the greatest chance of accomplishing our cause.