I think I only got one advanced summon spirit when I played through the game. I raised it to the first level cap and then stopped using it after that. Some of the problems are:
Unless you spend a lot of destiny orbs to do many summons, you'll probably end up having to use jokers to break the level caps.
You can only trade advanced summon spirits for other advanced summons, so there is no way other than spending destiny orbs to get more of them.
In many cases, a normal spirit with full pure merge bonuses will be more useful than an advanced spirit with no bonuses.
Here are some other tips based on my experience with the game:
Consider building up a set of element change spirits. You're in the Europe region, so you should be able to get Pandora ® for wood and Incubus (UC) for metal. You can also unlock Ghost Ship ® for water by clearing one of the zones near Australia and Chameleon (UC) for fire by clearing one of the zones in Africa. To get an earth element changer or R/SR spirits for metal and fire you'll need to trade or get lucky hunting. Using an element change spirit as the lead, you can field your best spirits against a boss and have an elemental advantage. Try to build up the pure merge stats for your R or lower spirits. If you merge a spirit of the same type any time other than when you're breaking the level cap, you'll receive some bonus stats for HP, attack, and speed that show up in parentheses. The more pure merges you perform, the higher these stats will go until they reach a cap determined by the spirit's rarity class. With full bonus stats, a UC spirit may be competitive with an R spirit with no bonuses, and similar for R spirits competing with SR. You can try building up bonus stats for SR spirits, but I ended up using most of my duplicate SRs for level breaks. The time stop skill is probably the most useful one in the game. Unfortunately the best time stop spirits were either from a limited summon promotion (Lady of the Depths can stop all enemies for 12 seconds for a cost of 50) or from a past event (Verdandi can stop one enemy for 15 seconds for a cost of 62). This can be invaluable during boss fights.