Thesaurus:augment

• add    [⇒ thesaurus]
• amplify
• augment
• dilate
• eke / eke out
• elevate
• embiggen (nonstandard, usually humorous)
• enhance
• enlarge
• enlargen (nonstandard)
• enrich    [⇒ thesaurus]
• greaten
• grow
• increase    [⇒ thesaurus]
• increment
• largen (UK, literary)
• magnify
• propagate (obsolete)
• raise
• strengthen
• swell
• up

• contract
• dial back (idiomatic)
• diminish    [⇒ thesaurus]

• alter    [⇒ thesaurus]

By filling with gas:

• blow up
• inflate
• pump up

By degree:

• maximize
• max out

In a single dimension:

• deepen
• lengthen    [⇒ thesaurus]
• widen    [⇒ thesaurus]

With respect to time:

• skyrocket (idiomatic)

Other:

• blow up
• improve    [⇒ thesaurus]
• speed up    [⇒ thesaurus]
• strengthen    [⇒ thesaurus]