Through personal experiences i have found that using the knowledge of your shared interests is the most helpful when trying to bridge the gap between acquaintances you may occasionally meet at miscellaneous networking events" and friends.
When using this information to come up with "excuses" I would suggest doing so in steps over time, where your invitations gradually become more and more personal which gives each of you more of a chance to gain that mutual understanding that you both enjoy the others company.
These steps should be refined and adapted to your personal situation but here is an example of what I would do:
First draw attention to the fact you are hoping to see them at an event you are both already going to. This first step is the most nerve wracking still important and choosing an event you are both already attending helps relieve the pressure for you and the other person.
Hi, I just heard about {%insert social event} (will you be attending?)/(i hope to see you there)/(i have this {%insert shared interest} to show you)
Next invite them to a new event they aren't attending of a similar nature.
My colleague told me about {%insert new event} I was wondering if you wanted to go and check it out with me?
After inviting them to a few of these, try to bridge the events into something more personal where the goal is to hang out with them rather than attend the networking event.
Did you want to meet up and have coffee or something before going to the event?
Eventually disregarding the event entirely where asking them if they want to hang out feels natural. The key here being that people feel more comfortable with things that are familiar to them. So slowly leaning into it can help reduce that awkward feeling, doing all of this may be a bit excessive and some of the steps could be unreasonable in your situation. Skipping some or all of the build up and going straight to asking someone to hang out is still totally fine! So please, after meeting someone you would like to befriend, push through the awkward and anxious thought that makes you hesitate and simply make an offer to follow up, however clumsy or embarrassing it may be and you will find that many people are delighted by the idea of hanging out with you again.