Empowered Spell - this metamagic ability allows you to reroll low damage dice. Not exactly what you want, but useful.
Elemental Affinity - Under the Draconic Bloodline origin, this class feature lets you add your CHA bonus to the damage of spells that do a specific damage type. Ashardalon's Stride does fire damage, so if you pick the right dragon type (i.e. red or gold), you can add your CHA bonus to the spell.
Spell Bombardment - Under the Wild Magic origin, this lets you get an additional die of damage, if any die you roll has the max value (so roll a six and get more damage). This is an 18th level class feature and is kinda random.
Elemental Adept - Select this feat with the fire option and your fire spells do a minimum of two damage per die and ignore resistance. Again, doesn't increase the max damage, but good to increase the overall damage.
Contagion - The Flesh Rot variety of this fifth level spell gives the victim vulnerability to all damage. But you would have to get a cleric or druid to cast it, or get a magic item the inflicts it.
Geas - Another bendy answer, but you could geas a target with the instruction "don't get burned", then the next time that creature takes damage from Ashardalon's stride, they also take the 5d10 psychic damage. If you are a wizard using stride, you could also know geas, otherwise you need to get someone else to cast it, like contagion.
Glyph of Warding - put explosive runes on yourself with the trigger "inflict damage with Ashardalon's stride". Warning, this will damage you, too.
Hallow - can also give energy vulnerability, but it is more of a defensive spell.
Web burns for 2d4 damage to anyone in the same square. But a strict reading of web and Ashardalon's stride would seem to indicate they don't mix (stride damages creatures or unheld items, webs may not qualify if they are in the square with a creature). Your DM may or may not allow it.
These are the only options in the PHB and Fizban's, which are the only two books I have onhand at the moment.
(might want to make this a community answer).