Strengthening agents and processes for making and using same

A process for making a paper product, comprising:

• combining a plurality of fibers and water to produce a slurry;
• forming the slurry into a wet paper web;
• pressing and draining the wet paper web to produce a wet paper sheet, wherein a strengthening agent is (i) combined with the plurality of fibers and water to produce the slurry, (ii) applied to the wet paper web, (iii) applied to the wet paper sheet, or (iv) a combination of at least two of (i), (ii), and (iii), and wherein the strengthening agent comprises a polyamidoamine-epihalohydrin resin and an additive, wherein the additive comprises at least one of a tannin and a compound having a chemical formula (I) comprising:
• wherein:
• R1, R2, and R3 are independently a hydroxyl group or a methoxy group, and R4, R5, and R6 are independently H, an alkyl group, an aldehyde group, a carboxylic acid group, or a —C═C—COOH group;
• and
• drying the wet paper sheet to produce the paper product.