You don't have multiple foreign keys. You have things reminiscent of FKs. A FK is a column set whose subtype values are always also in another table where the columns form a candidate key. As commented your design is an anti-pattern because it is needlessly complicated. And SQL doesn't easily support its integrity or its optimization.
Instead of having columns type and foreign_id [sic] in table info where type value indicates which other table that it must appear in as an id value it is straightforward to have a table VALUE_info for each value permitted in type with a FK foreign_id to the appropriate VALUE_other table id.
However it's possible that what your really need is each VALUE_other table to have its foreign_id column be a FK referencing info. Ie you might want the FK going the other way. This happens when info(id,type,...) means "thing [id] is of subtype [type] and ...) and VALUE_other(foreign_id,...) means "thing [foreign_id] is of subtype VALUE and ...". Notice that the proper names are then thing_info(id,type,...) and VALUE_thing_info(id,...). You might not want type any more. Things similar to this might all be set up automatically by an ORM that has explicit support for "subtyping" or "polymorphism".
If this suits your needs then in this particular case of subtyping since you were able to have every row of info have a foreign_id FK to one VALUE_other table it means that every thing is of exactly one subtype. For at most one subtype you can write an SQL constraint for each VALUE_thing_info table that an id's matching row in thing_info has a type value of VALUE. (Technically type is still redundant in the database but it can help with clarity and efficiency.) You can write an SQL constraint that the thing_info id values are in the union of the VALUE_thing_info id values. (Some such constraints can be declarative. Having type in thing_info helps with that. Putting type also in the VALUE_thing_info tables is another more redundant idiom that however can also help being more declarative. Although constraints on updates can be faster.)