The lackadaisical quantum walk, a quantum analog of the lazy random walk, is obtained by adding a weighted self-loop transition to each state. Impacts of the self-loop weight l on the final success probability in finding a solution make it a key parameter for the search process. The number of self-loops can also be critical for search tasks. This article proposes the quantum search algorithm Multi-self-loop Lackadaisical Quantum Walk with Partial Phase Inversion, which can be defined as a lackadaisical quantum walk with multiple self-loops, where the target state phase is partially inverted. In the proposed algorithm, each vertex has m self-loops, with weights l′=l/m, where l is a real parameter. The phase inversion is based on Grover's algorithm and acts partially, modifying the phase of a given quantity s<m of self-loops. On a hypercube structure, we analyzed the situation where 1⩽m⩽30. We also propose two new weight values based on two ideal weights l used in the literature. We investigated the effects of partial phase inversion in the search for 1 to 12 marked vertices. As a result, this proposal improved the maximum success probabilities to values close to 1 in O((n+m)⋅N), where n is the hypercube degree. This article contributes with a new perspective on the use of quantum interferences in constructing new quantum search algorithms.