Yes, this is called a "quantum non-demolition measurement" and has actually been done. One technique is to use highly excited atoms (Rydberg atoms) which are ex

Yes, this is called a "quantum non-demolition measurement" and has actually been done. One technique is to use highly excited atoms (Rydberg atoms) which are extremely sensitive to external electric fields. In this way, the field caused by a single photon can be detected without absorbing the photon. There is a famous paper from Serge Haroche's group where they used this method to detect the presence of single microwave photons in a superconducting cavity (https://www.nature.com/articles/nature05589 https://www.nature.com/articles/nature05589). However, the measurement still collapses the wavefunction of the system. Performing a QND measurement to determine which slit the photon takes in a double-slit experiment simply destroys the interference pattern.