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Are there any larger implications of allowing a variant rule Ability Score Improvement/Feats in a multi-classing campaign?

In one campaign we have all multi-class players. There has been a frustration about having to take a 4th or 8th level in a class for the sole purpose of having access to an Ability Score Improvement (ASI) or a Feat.

I want to suggest we have a character level progression system instead of class, when it comes to ability score improvements and feats. This seems simple enough. The majority of classes get an ASI or feat at levels 4, 8, 12, 16 and 19 - with the exception of a Fighter who also gets this at levels 6 and 15 and a Rogue who gets it at level 10.

The variant rule would be that a PC gets the option of an ASI/feat when it reaches character levels: 4, 8, 12, 16 and 19. If the player chooses to develop into the Fighter/Rogue class, then that PC would get an ASI/feat upon reaching Fighter level 6 and 14 or Rogue level 10.

There is a similar mechanic with cantrips for multi-classing players, where the upgrades depend on overall character level, rather than class level (PHB, p.164).

Variant Rule: Ability Score Improvement, or Feat

When you reach 4th level on your overall character level, and again at 8th, 12th, 16th, and 19th level, you can increase one ability score of your choice by 2, or you can increase two ability scores of your choice by 1. As normal, you can’t increase an ability score above 20 using this feature. The increase is based on your character level, not your level in a particular class. Using the optional feats rule, you can forgo taking the Ability Score Improvement feature and take a feat of your choice instead.

In addition: if you train as a Fighter, you get an Ability Score Improvement at upon reaching 6th and 14th level in that class; or at level 10 if you train as a Rogue.

Would this create any great unbalance? I can't see it, but I might be missing something.

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    \$\begingroup\$ Also closely related Would these multi-classing house rules cause unintended problems? \$\endgroup\$
    – Tiggerous
    Mar 6, 2020 at 10:44
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    \$\begingroup\$ To clarify - would this push back / replace any class features the PC was otherwise due to gain that level, or be in addition to them? \$\endgroup\$
    – Tiggerous
    Mar 6, 2020 at 10:49
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    \$\begingroup\$ I appreciate the Question/Answer has really helpful information, but that is not quite the Variant rule I am suggesting. Can you please re-open so it can be answered? \$\endgroup\$
    – Senmurv
    Mar 6, 2020 at 18:43
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    \$\begingroup\$ I'm having a very hard time parsing the difference. In the linked question it's about providing ASIs every 4 levels and not 4 class levels. Yours is the same, no? \$\endgroup\$
    – NotArch
    Mar 6, 2020 at 18:50
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    \$\begingroup\$ Again, i'm having trouble with the nuance. Both questions are about character level ASIs and not Class level ASIs. The fact that you're accounting for two classes that get them more often doesn't really seem to change that. in fact, the current dupe also covers that the fighter/rogue would still get theirs, which yours does, too. \$\endgroup\$
    – NotArch
    Mar 6, 2020 at 18:55

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