It sounds like you already have a well-functioning department, without interpersonal problems, so be careful that any changes don't make it worse. Thus, I would suggest approaching the problem with caution, being careful that anything you add is not creating unintended consequences. Having said that, here are some suggestions (I am nowhere near HoD level, so take these as the advice of a novice):
Social occasions are okay, but don't expect them to affect happiness: Having two social occasions per year sounds about right to me. It is nice to have some socialisation at the workplace, during regular work hours, but too much can make it feel like a time-competitor with work you need to do, or you can simply run out of things to talk about. Unless the people in your department are actual friends, the social occasions are likely to consist of the kind of surface-level conversations you get among colleagues. Many employees prefer to allocate their social time to friends that they have had since earlier in their life, whom they are closer to.
Regardless of how good the social occasions are, I find that my own happiness in an academic department is barely affected by them. I feel happy when I am successful at work (e.g., good work productivity, outputs, etc.) and I feel unhappy when I am struggling (uncompleted work dragging on, etc.). Having a wine-mixer is not going to help in the latter case.
Implement a proper mentoring system: Some answers have suggested salary increases, but that would come with a major financial cost. Also, for researchers like me, who are below full-professor level, I think we mostly want to try to improve our performance and earn salary increases through the standard academic progression (e.g., progressing from assistant-prof to associate-prof, to full-prof). Bonus money is certainly nice, if it is available, but genuine long-term progression in performance, and subsequent promotion and salary increase based on merit, is much more rewarding.
In view of this, a helpful thing to do, if you haven't already got something like this, would be to establish a proper mentoring system to really genuinely help all your lower academics (anything below full-professor) with mentoring by the senior professors. Allocate time to have a senior mentor sit down for a sustained period of time with us and learn about our research work, make plans and career goals, help us with how to produce better quality research more productively, get competitive in grant applications, get citations and interest in our work, etc. Even just having a regular pep-talk with a senior colleague, checking on progress, is helpful.
Allocate time to skill-sharing (and count this as part of teaching load) Too often in academic departments, I find that you are mostly just in your own office, hacking through the wilderness on your own research projects and teaching. You are surrounded by people with amazing skills, but there is usually no systematic attempt (and no incentive) to spread these skills around. One teacher wins a teaching award while another is having trouble with teaching, but never shall the twain meet! One academic is a wizard on computer software used in discipline research while others find it bewildering, yet they never sit down to transfer this skill.
It would be wonderful if there was time allocated for academics to teach each other and spread their skills around. If you have any academics that are great teachers (e.g., teaching awards, etc.), give them a small amount of time-credit on their teaching to allow them to sit down with other academics (either one-on-one or in small groups) and pass on their best skills and advice. If you have any academics that are wizards on computational software used in the discipline, give them some time-credit to teach these skills to three or four other academics. If you have some quality teachers, give them some time-credit to assist other academics in improving their teaching.
Impose strict discipline in meetings: Academics are the worst people in the world at meetings. Compared to meetings in the corporate world, academic meetings are excruciating (and even the corporate world is pretty bad). Formal meetings should have an agenda, and should progress through the points in the agenda at a reasonable speed. No bull-sessions of rambling tangential discussion that take an hour (for something that could be done in ten minutes). If someone starts rambling on about a tangential issue, the meeting chair needs to interject and remind participants that people's time is valuable, and get the discussion back on track.