This　paper　studies　adaptive　radar　detection　of　point-like　targets　in　the　presence　of　Gaussian　interference　and　possible　diffuse　multipath.　For　this　problem,　a　Tunable　Adaptive　Matched　Filter　(T-AMF)　detector　which　contains　a　tuning　parameter　ruled　by　the　strength　of　multipath　effects　was　proposed.　This　paper　develops　a　two-stage　strategy　for　the　selection　of　the　tuning　parameter　by　jointly　using　a　two-step　energy　detector　and　the　expected　likelihood　(EL)-based　principle.　Once　plugged　into　the　T-AMF,　the　selected　parameter　yields　a　fully　adaptive　detector　free　of　any　user　parameter.　Remarkably,　the　new　architecture　possesses　the　desired　constant　false　alarm　rate　(CFAR)　property　with　respect　to　the　disturbance　covariance.　Finally,　its　detection　performance　is　assessed　and　validated　via　numerical　examples.　©　2020　IEEE.