Saeko will likely be one of the first Party members you will max out. She has a bond level that is increased via the usual methods (Battle, Meals together, Karaoke at Survive, Random Chats around town, Seagull Cinema and Gifts).
In the Party screen you select her and "Check Bond" which will tell you if she is ready to level up your relationship at Survive Bar on the far-western side of the map. She will max out at level 5 and there are no barriers to progressing her Bond level once you have her in your party.
You will have a final task for the Rank-up portion for Rank 5: