Ok, so here is an Email that I sent to my group concerning this house rule (I wrote some other stuff, but this is the rules / examples / limitations section). I think that the limitations listed at the bottom of this do balance out the higher level spell casting capability quite a bit and does open up multiclassing to a wide number of class combos which normally would never be created.
Instead of using the chart for the class to determine which spells can be prepped, the multiclassing chart is used to determine which spells can be prepped, similar to how the multiclassing chart is currently used to determine which spell slots are available. This allows the PC to not fall behind on his spell casting levels, just because he decided to multiclass a little (or even a lot). However, this rule does need a throttle on it because otherwise, a Wizard 1 / Cleric 6 could cast 4th level spells in both classes. The throttle is that for PCs who do that, two new numbers are added to their character sheet: Spell Points for Class 1, Spell Points for Class 2. So, we multiple the number of first level spells by one, the number of second level spells by two, etc. to determine the total number of spell points. Those points are then divided by the two classes to determine how many spells can be cast from each class based on how many levels that class adds to the multiclassing spell level. Also, the PC can exceed the highest level spell he knows in each class.
For example:
Wizard 1 / Cleric 6
Cleric 7 can normally cast 4 1st, 3 2nd, 3 3rd, and 1 4th level spells. W 1 / C 6 can also cast that many spells, but the class has no 4th level spells and hence falls behind other 7th level PCs a bit.
There are a total of 23 spell points here (4 * 1 + 3 * 2 + 3 * 3 + 1 * 4). 1/7 of those points go to Wizard, so 3 Wizard spell points and 20 Cleric spell points.
So, the PC can cast 3 first level Wizard spells, one 1st and a 2nd, or 1 3rd level spell. The PC can also cast a 4th level Cleric spell and doesn't fall behind other PCs.
Example 2:
Wizard 6 / Cleric 6
The PC can cast 4 1st, 3 2nd, 3 3rd, 3 4th, 2 5th, and 1 6th spells. There are 35 SP so 17 Wizard SP and 18 Cleric SP (the remaining point goes to whichever class was created at first level, so normally this would be cleric)
The PC can cast a single 6th level spell. If he casts it as Wizard, he now has 11 Wizard SP and 18 Cleric SP.
Example 3:
Ranger 4 / Paladin 6
The PC can cast 4 1st and 2 2nd spells. There are 8 SP so 3 Ranger SP and 5 Paladin SP.
The PC can cast two 2nd level spells. He can use those two slots for one Ranger and one Paladin, or two Paladin slots. With the PHB rules, this PC would be limited to first level spells.
Example 4: Everett (Everett is a PC that was created when 5E first came out and we had limited understanding of the rules. The player felt like he lagged behind other PCs casting-wise and his Ranger abilities did not make up for that.)
Ranger 2 / Wizard 10
The PC can cast 4 1st, 3 2nd, 3 3rd, 3 4th, 2 5th, and 1 6th spells. There are 35 SP, but this PC is level 11 on the multiclassing spell chart, not level 12 (unlike classes that are full casting classes, Ranger is 1/2 casting level, 10 levels for Wizard, 1 level for Ranger). There are 35 SP with 1/11 Ranger, so 3 Ranger SP and 32 Wizard SP.
With the normal PHB rules, Everett could have cast as many first level Ranger spells as he wanted to, putting them into higher level spell slots. He could cast Cure Wounds over and over and over again. With this houserule, he can cast a max of 3 Ranger spells (it's a limitation, see below). On the other hand, Everett could also know and cast a 3rd level Ranger spell. Since 2nd level Rangers only get two total spells known, he would have to decide whether he wanted to know 2 first, 1 first and 1 second, or 1 first and 1 third (he could also do 1 second and 1 third, but then he could only cast one Ranger spell per day). He can cast higher level spells, but fewer Ranger spells overall per day. On the other hand, this PC can cast a 6th level Wizard spell.
You might ask, what are the downsides of this? Well, there actually are some that might not be obvious. This is not just free higher level spells, it has a cost.
1) MAD (multiple attribute dependency). In order to do this type of thing, the PC typically needs a 13 in two different ability scores which are not CON or DEX. So for example, having a 16 in Wis at level 1 and putting a 13 in Int means that 5 point buy points were used for Int instead of for Con or Dex or something else. This means maybe slightly lower AC, or slightly lower hit points, and maybe -1 in one or two saving throws. It gets even worse if the PC wants to have a decently high score in both Wis and Int to get good spell DCs and such.
2) ASI delay (Ability Score Improvement). ASI is that feature at levels 4, 8, 12, etc. where you get to buy a feat or bump up an ability score by 2 points. When multiclassing, those ASIs are delayed because although the PC might be able to cast slightly higher level spells than normal, he doesn't get the features of that slightly higher level PC in that class. In addition to this, the player already wants to bump up two spell casting ability scores, so delaying that many levels does throttle down how high save DCs and such are.
3) Other class feature delays. Bard 1 / Sorcerer 2 might be able to cast 2nd level Sorcerer spells, but the PC does not yet get metamagic. The PC is not truly a 3rd level Sorcerer.
4) Not necessarily able to cast all spells every single day. This doesn't always happen, but it could. In the Wizard 5 / Cleric 5 example, the PC could cast all of his spells but one single 4th level spell. He has 1 Wizard SP left over and 3 Cleric SP left over. He cannot cast a 4th level spell with either class, so he loses the spell slot. At the beginning of the day, the PC can cast whatever spells he wants. Near the end of the day, things get a little more restrictive. The PC might have to limit which spells that get cast, or he might end up in a situation where one spell slot gets lost. And, that's ok. It's the cost of being able to cast slightly higher level spells in both classes.
5) The ratio of spells cast is based on how many levels (that apply to the multiclass table) in each class. So instead of being able to cast all spells from one class, each class gets fewer spells cast per day in order to compensate for the ability to cast higher level spells. In a Wizard 6 / Cleric 6 scenario, half of the spells must be Wizard spells and half must be Cleric spells.