Items for AP Mages

Hello everyone! I'm writing here because i want to discuss about items for ap mid champions. Currently core items for every ap mid champ are rabadon, zhonya and void staff. It's pretty annoying because i can choose only 2 different items (except boots) to buy, according to champion i'm playing. Let's think about {{champion:69}} for a while. I wish I bought different items which would replace one or two of core three items but i worry that my Cassio would deal less damage with different items than 3 above-mentioned. I wanted to buy for example: tear -> serafin, rylai + liandry, void staff or abyssal (it's sad that i can choose one of both, instead of building both) and luden's echo. This build gains movement speed, magic penetration, double damage from liandry's passive (because of rylai), mana (core for Cassio) and higher damage from luden's echo every few seconds. With this build i wonder that she may deal less damage without rabadon and zhonya (cuz of massive ap from these items). My questions are: Do i have to build these 3 core items on every mage? What about damage if i buy some different items? (math needed) When should i buy individual items? Thanks for the answers :)
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