Multivalent interactions involve the engagement of multiple ligand-receptor pairs and are important in synthetic biology as design paradigms for targeted nanoparticles (NPs). However, little is known about the specific ligand parameters important to multivalent interactions. We employed a series of oligonucleotides as ligands conjugated to dendrimers as nanoparticles, and used complementary oligonucleotides on a functionalized SPR surface to measure binding. We compared the effect of ligand affinity to ligand number on the avidity characteristics of functionalized NPs. Changing the ligand affinity, either by changing the temperature of the system or by substitution noncomplementary base pairs into the oligonucleotides, had little effect on multivalent interaction; the overall avidity, number of ligands required for avidity per particle, and the number of particles showing avidity did not significantly change. We then made NP conjugates with the same oligonucleotide using an efficient copper-free click chemistry that resulted in essentially all of the NPs in the population exceeding the threshold ligand value. The particles exceeding the threshold ligand number again demonstrated high avidity interactions. This work validates the concept of a threshold ligand valence and suggests that the number of ligands per nanoparticle is the defining factor in achieving high avidity interactions.