The Herald’s political editor Magnus Gardham noted in his column last weekend: “For weeks we've been told this was the most boring Holyrood election ever. In fact, it's been the most interesting.”

The SNP losing its majority certainly opens up all sorts of possibilities that were previously closed down. It’s no surprise that headline writers have been reaching for some old favourite cliches, involving people offering olive branches, helping “prop up” others and striking deals.

Print and social media have both seen a flurry of spurious claims about deals already done, between any combination of parties, on anything from another independence referendum to future budgets which aren’t even written yet.

Parties are being accused of offering support to the government on tax rates, fracking or the much-misrepresented Named Persons scheme, despite their policies remaining entirely unchanged from before the election.

In reality of course, everyone’s still digesting the result of the election. But it’s inevitable that there’s gossip to be heard about how this new Parliament will change, with ministers unable to rely on a loyal majority.

Holyrood itself is in need of reform, as people across the political spectrum acknowledge.

The tinkering at the edges we’ve seen in recent years isn’t enough. The committee system needs strengthening to provide better scrutiny of government proposals, and greater public involvement is needed, recapturing the spirit of “a parliament that shares power with the people”.

We must also improve set-piece events such as First Minister’s Questions. Limiting this slot to six questions, with two party leaders dominating the first 15 minutes of a 30-minute session, simply doesn’t reflect the variety of issues and political opinions our parliament should be airing.

As for how the government itself operates, we should consider where the parties stand in terms of policies and how MSPs have voted on legislation in previous sessions.

For example, the Scottish Greens clearly support the idea of an independent Scotland.

We believe the timing of when Scotland asks itself the question again should be for the Scottish people to decide.

Parliament retains a pro-independence majority but our case must be strengthened to address some of the weaknesses evident in 2014 such as those around currency.

Yet while that work remains to be done, it may suit the Tories in particular to keep the constitution uppermost in everyone’s mind, while simultaneously demanding that everybody else “move beyond” it.

My newly-elected MSP colleague Andy Wightman was told by the postie delivering his parliamentary credentials that he had voted Green to ban fracking and scrap the council tax.

Greens ensured through the Smith Commission that power over fracking licences was devolved to Scotland, and we intend to continue pushing the SNP to turn its temporary moratorium into a permanent ban to protect our communities and meet our climate change obligations.

The SNP’s faith in the unfair, outdated council tax must also be questioned, and I believe there’s an opportunity to do so given the shift in position on local taxation in recent weeks by Labour and the Liberal Democrats.

And take Air Passenger Duty. There’s clearly not a majority in parliament in favour of the SNP’s policy of halving, then scrapping, Air Passenger Duty. Let’s look at this as an opportunity to resolve what is a complex issue.

In the past Greens have suggesting models such as the Frequent Flyer Levy. This would ensure the cost is shifted onto the minority of mostly wealthy individuals who fly most often. The SNP’s proposal would add to climate change emissions and do nothing to tackle social inequality. Instead we could create a new way forward that recognises the environmental impact of aviation and ensures the right people pay the lion’s share.

Minority government can achieve a lot. In 2007 the Climate Challenge Fund was formed as part of a budget agreement between the SNP and the Greens. To date it has awarded £75.7 million, empowering 588 communities to tackle energy efficiency, food, transport and waste. It’s a modest example of what is possible when parties work together.

Let’s hope we see even bolder ideas coming to fruition in the months and years ahead.

Patrick Harvie MSP is co-convener of the Scottish Greens.