HO to itself is called intra-cell Hand Over. This feature has to be enabled on the cell.
The signal level of the neighbor cell being high all the time is still subject to the Ranking criteria that has to be met by the Neighbor cell. The question is, does the Neighbor cell able to meet the criteria and be the 1st in the neighbor ranking? Furthermore, there are parameters that limits the HO from higher band cells to the lower band cells (say from 1800 to 900 bands). If in case they are in the same band, there may be layers within the band that has to be considered also on the ranking process before the HO decision to any cell is executed.