GA pilot reported an NMAC entering the SUZ traffic pattern resulting in evasive action.

Narrative

While flying a vfr practice approach into SUZ (ILS 2) I gave radio calls before the initial fix at the initial fix (REMBE) and inbound after the procedure turn on the crag including plane; location; and altitude. Another plane Aircraft Y was approaching from the southwest and gave a call inbound to SUZ. At this time I was established inbound on the ILS 2 and gave an additional call of location and altitude. I was able to spot Aircraft Y at my 9 o'clock and approximately 2 miles and 200 ft below me. I called the call sign and the pilot acknowledged me that he didn't see me so I gave him my position relative to his and what I was doing. Very shortly thereafter he turns to his right directly at me with us now at a very similar altitude; to avoid another plane in the area. In doing so he was directly in my path and I pitched up and climbed while adding full power. Also asked him if he could see me and for him not to climb or he would hit me. If I had not taken this action there would have been a mid air collision. I broke off the approach and followed Aircraft Y to the left down wind for 20 and landing was normal. At no time did it appear that this pilot saw me or tried to avoid me in his maneuvering between myself and the other plane that he did see. ADS-B did give me a warning that he was 200 feet below me and 0 miles when he passed under me.