Can more than one conditional proof be used in an argument?

Briefly yes, it is permissible to use C.P. more than once in a given formal proof. But either one must be “nested” fully within the other, or they must be completely distinct. They cannot “overlap.” Here is an example for an interesting argument:

1. (P ∨ Q) ⊃ R   /  ∴  (P ⊃ R) • (Q ⊃ R)
2. P                    C.P.A.
3. P ∨ Q           2 Add.
4. R                    1, 3 M.P.
5. P ⊃ R           2-4 C. P.
6. Q                   C.P.A.
7. Q ∨ P           6 Add.
8. P ∨ Q           7 Com.
9. R                    1, 8 M.P.
10. Q ⊃ R           6-9 C.P.
11. (P ⊃ R) • (Q ⊃ R)    5, 10 Conj.

Q.E.D.