Generally, vaccines contain two distinct parts: the active ingredient and the added ingredient.
The main antigen that elicits the immune response is the active ingredient and it is highly biological in nature. It might be the attenuated virus particle, an mRNA, or inactivated virus (or bacteria) depending on the type of vaccine.
The added ingredients make up the rest of the vaccine including adjuvants and the carrier of the vaccine. Adjuvants, emulsifiers, and taste improvers (for oral vaccines) are added ingredients.
Aluminium salts are the most widely used adjuvants; and the adsorption of these salts to the antigen has been found to be driven mainly by electrostatic, hydrogen-bonding, van der Waals and hydrophobic interactions. Since aluminium salts based adjuvants are not directly covalently bonded to the antigen, it might be possible to detach them by using different ionic/pH modifications. If this could be done, then we could detach the adjuvant salts, purify them and reuse them for new vaccine formulations.
Another adjuvant system that is used is emulsion based, though less frequent. Emulsions such as oil-in-water, water-in-oil, water-in-oil-in-water and proten-stabilized emulsions are used as nanoparticles to stabilize and enhance vaccines. For such vaccines, phase-separation can be used to separate the components and collect them.
These are just some possible ideas and I am not entirely sure if they are feasible. At least in theory, they seem possible to me.