What house rules do you have for multiclassing? What prompted you to use them? What effect have they had on your games?
1. No favored classes.
3. No multiclassing restrictions.
2. No PrCs
4. Spellcasters advance spellcasting by advancing noncasting classes at a rate of 1/2.
5. Special feats allow you to also sum other spellcasters to the lot.
We clearly have different goals here. I'm trying to make races much more differentiated. Likewise, I consider the fact that humans have relatively few multi-classing restrictions one of their main advantages, and if you remove it you more strongly move the game toward a non-human world.
On the other hand, we agree on this. Very few people inclined to write house rules for 3e disagree. The PrC stands out as the single biggest mistake in the 3e rules.
I first read #4 and I was like, "What? No way. Clearly he hasn't play tested at all.", but then I read your more detailed explanation and was like, "Yeah, ok. That works." The rule actually reads:
"4. Spellcasters advance spellcasting by advancing noncasting classes at a rate of 1/2 to a maximum of 1/2 their class levels in the spellcasting class."
This does the same job and ends out working rather similarly to my system in terms of the actual caster levels you can actually obtain through multi-classing, except that in my case the sort of advantage gained in #4 itself comes to you by way of special feats. Your system on the other hand offers a bit more protection from primarily non-casters dipping a level or two of caster in order to gain spells, or primary casters dipping for a level or two of non-caster with no loss in spell casting ability. You also provide more support for low level gishing below 3rd level - ei, a Ftr2/Wiz1 or Ftr2/Wiz3 is probably more viable/balanced in your system than mine, though mine can demonstrably work and gets a much bigger boost than yours at Ftr2/Wiz4 when the additional general feat becomes available. Likewise, your Ftr4/Wiz16 is giving up more than mine (but in practice perhaps enough you'd never see it actually happen), and my Ftr16/Wiz4 is gaining more at less cost (again, yours gains so little that I'm not sure it would ever happen). I'm not sure how I feel about all that, as the problem in my system is mostly theoretical, the actual realized power level differences are small, and I'm hesitant to change in my system what isn't clearly broken. However, the fact that you are producing these results naturally to me suggests that your system is likely to be at least as robust when playtested as mine has been, and in general I'm less worried about your system getting busted in the edge cases than I am about mine getting busted. Your idea to introduce things as capped ratios seems solid.
Sure thing, but they never came up with a decent alternative that would enable them to throw PrCs out the window without losing character concept flexibility.
Monte as he originally conceived them saw the PrC as a way to convey the flavor of major NPC driven organizations.
Also in practice, the PrCs Monte created had the problem that every member of an organization was typically the same character.
They were an attempt to patch the balance between casters and noncasters by giving noncasters more robust options.
They were an attempt to patch problems with the baggage carried by core classes to allow for choices that the core classes didn't allow for.
What if you wanted a ranger that wasn't a spellcaster? Or a ranger that was suited to an urban environment?
WotC began to print PrCs that actively undermined its own game system. They were cheap to make as long as you didn't play test them (imagine, not play testing a class in a class based system), as witnessed by the hordes that appear in 3rd party supplements.
I think the decent alternatives are suggested by something like your multi-classing fix, plus...
a) Broader embracing of the feat and what a feat is allowed to do, particularly in a more 5e style. For me this realization occurred when I realized that every PrC was simply a feat chain generally geared to a particular class which had as its requirements the requirements of entering into the PrC.
b) General rebalancing of the core classes. For me a lot of that has involved a combination of thinking about class abilities in terms of 'feat equivalents' (if every feature of this class was bonus feats, how many feats would the class features be worth), toning down the power of spells/spell-casters while increasing the power of feats and skills (and those that rely on them).

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.