We study the generation of high-order harmonics from plasma plume, by using the 20 TW, 10 Hz laser of the Advanced Laser Light Source (ALLS). We perform detailed studies on enhancement of single high-order harmonics generated in laser plasma using the fundamental and second harmonic of the ALLS beam line. Quasi-monochromatic harmonics are observed for Mn, Cr, Sb, Sn, and In plasmas. We identify most of the ionic/neutral transitions responsible for the enhancement, which all have strong oscillator strengths. Intensity enhancements of the 13th, 17th, 21st, 29th, and 33rd harmonics from these targets are demonstrated using the 800 nm pump laser and varying its chirp. We also observed harmonic enhancement from some targets for 400 nm pump laser. Using Mn plume, we demonstrated the highest harmonic photon energy (52.9 eV) at which enhancement has been observed (17th order, λ = 23.5 nm).