Tonal harmony does provide some ways to further develop harmonic patterns in blues, but with some specificities.
The secondary dominant is a concept borrowed from classical harmony that's widely used in jazz blues. This may be taken an additional step further with the commonly used in Jazz ii-V-I progression.
So, for a basic 12 bar blues progression
I I I I
IV IV I I
V V I I
We can introduce a ii-V-I (applied to the concept of secondary dominant, secondary sub-dominant or, more generically "local key") for each change in harmonic function:
I I I ii/IV V/IV <--- ii-V-I to approach the subdominant
IV IV I I
ii V I I <--- here we already have V-I, just add the ii before the dominant
Further harmonic development can be:
I IV I ii/IV V/IV <--- simple I-IV-I- progression
IV IV I V/ii <- secondary dominant to approach the ii
ii V I ii V <--- introduce "turnaround" with ii-V-I of the tonic proper
This is, I think, some times called a "basic blues progression", to distinguish from the more simple, so more generic blues progression.
As I understand, so far we have only used techniques that could have been used by any composer of the classical period, to introduce harmonic development and increase harmonic rhythm. As I said, secondary dominants, passing chords, and the ii-V-I progression is nothing more in essence than a circle of fifths progression.
The blues specificities come of course from the generic use of 7th chords in all scale degrees and chords, and the voice leading applied. Not that the general classical rules of voice leading (keep common tones, move by steps, etc.) are not generically followed, but because of the special focus given to the so called guide tones (the 3rds and 7ths of all chords).
So, to be clear, let's put the example in chord names, for example in C, rather than roman numerals:
C7 F7 C7 Gm7 C7 <-- C does not function here as tonic but as dominant of F
F7 F7 C7 A7 <-- A is dominant of D
Dm7 G7 C7 Dm7 G7 <-- initial Dm anticipates the coming of the dominant proper, G
Harmony can be further enriched by chromatic substitutions, again, the same basic idea as in classical harmony: finding chromatic neighbours for passing chords, etc. But I'm afraid I'm still trying to make my self at home with that part myself..