This is almost paradoxical, because if you focus too much on "planning" for alternative routes you ultimately tend towards constricting the number of available routes to exactly those you've planned for, achieving a pale semblance of your goal instead.
There is some level of specific design work you may need to do to facilitate this (for example, rooms in Rogue Legacy must have explicit extra paths added for heroes with dwarfism traits, levels in Fallout 3 often have lock-picking and computer-hacking paths to achieve some goal); you just don't want to take this so far as to end up always having "the path for this ability," and "the path for that ability."
The abstract techniques you should employ to allow for multiple paths and strategies in a game align closely with those you'd probably want to employ to foster replayability in general. This includes things like designing for composability:
give a player (eventual) access to many abilities, each of which do a relatively small thing on their own, and possibly have a small downside
approach the design of your gameplay space in terms of verbs and nouns: simple things that can be done, and simple things that can be operated on
don't artificially restrict those combinations, and let your playtesters explore, and listen to their feedback when they say "hey, I tried to use X to do Y here and I thought it would work, but it didn't."
if possible, design levels and areas to be true to their real-life analogues; players can relate to real spaces and their own internal fantasies of being (for example) a crazy parkour acrobat traversing an actual urban landscape, or a daring Lara Croft or Indiana Jones-like spelunker. Forming gameplay spaces around familiar structures allows players to more easily project those fantasies into the game and see options for exploration.
For example, grenade-hopping and the like is a direct consequence of two simple factors:
- explosions push things around in relatively physically-accurate way
- the player is tougher than most other things
These combine to make grenade-hopping a viable option, even if it wasn't designed into the game (by contrast, some sequence-breaking-enabling things, like the foam gun in Shadow Complex, were specifically designed into games for sequence breakers).
This sort of thing is a far more organic then premeditated process. Keep building simple composable gameplay elements and then trying them together yourself or through playtesters. See what they come up with; that may inspire you to add other abilities to further compliment a strategy you see emerging ("emergent gameplay" was the 90s buzzword for this sort of thing, incidentally). Or it may necessitate you adding downsides to abilities to complicate the exploiting of some mechanic you feel trivializes the game too much, or something.