When using multiple Research tokens in a single round, the draws and discards must be fully resolved one at a time before using the next token. The rulebook states:

"A player may use more than 1 Research token, as long as they complete the draw and discard actions for each token separately."
(page 5)

This means a player must:

• Discard a Research token,
• Draw 3 cards in any combination from the Tokyo and Kyoto decks,
• Immediately discard any 3 cards to the face-up discard pile,
• Only then may they use another Research token and repeat the process.

Players may not combine the draws and discards from multiple Research tokens for efficiency; each token's effect must be resolved in full before the next is used.

Source: page 5

Source: Base Rules (pp. 2, 3, 5, 7, 8)