Suppose you want to do 2d20 for ability scores, but don't have enough d10s. 
You can just do 2x proficiency bonus for all ability checks, and ~3x for expertise. That'll get pretty close.
Or, add both your proficiency bonus and a proficiency die. Which is fun. Expertise roll the die twice and take the better result.
+2: 1d4
+3: 1d6
+4: 1d8
+5: 1d10
+6: 1d12
The "success and magnitude" that you sometimes want can also leverage this. If you need a magnitude of success, you can take proficiency die plus attribute bonus (min 1).
Int 16 profi +2 goes from +5 to +5+1d4, which is about 1.5x
Int 20 prof +4 goes from +9 to +9+1d8, again about 1.5x
Int 14 and +6 prof (expertise) from +8 to +8+2d6 1.6x
Int 20 and +12 prof (expertise) from +17 to +17 +2d12 drop lowest is about 1.5x.
Int 20 and +6 prof from +11 to +11+1d12 1.6x.

You can just do 2x proficiency bonus for all ability checks, and ~3x for expertise. That'll get pretty close.
Or, add both your proficiency bonus and a proficiency die. Which is fun. Expertise roll the die twice and take the better result.
+2: 1d4
+3: 1d6
+4: 1d8
+5: 1d10
+6: 1d12
The "success and magnitude" that you sometimes want can also leverage this. If you need a magnitude of success, you can take proficiency die plus attribute bonus (min 1).
Int 16 profi +2 goes from +5 to +5+1d4, which is about 1.5x
Int 20 prof +4 goes from +9 to +9+1d8, again about 1.5x
Int 14 and +6 prof (expertise) from +8 to +8+2d6 1.6x
Int 20 and +12 prof (expertise) from +17 to +17 +2d12 drop lowest is about 1.5x.
Int 20 and +6 prof from +11 to +11+1d12 1.6x.
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