Applying a projector or a general nonunitary gate in the middle of a circuit using qiskit

Is there a way to implement a projector gate in a middle of a circuit?. For instance, assuming I have a Bell state $$|00\rangle+|11\rangle$$, I'd like to apply a projector on the first qubit onto state $$|1\rangle$$ (operator $$|1\rangle\langle 1|$$). Meaning that I will be left with $$|1\rangle|1\rangle$$.Is it possible to do such thing in the middle, and then apply the rest circuit? Also, is there a way to apply a general nonunitary gate without performing real measurements or qasm, only statevector.