The government is currently negotiating with the Lib Dems and Greens to strike a deal to get its budget plans passed.
Green co-convener Patrick Harvie has asked for concessions over tax, while Lib Dem Willie Rennie has targeted up to £400m of additional spending.
Finance Secretary Derek Mackay has said he is "positive" about winning support.
With the SNP a minority government, they will need at least one opposition party to help the budget pass, either by voting for it or by abstaining.
Mr Mackay has indicated a budget deal with the Conservatives or Labour is unlikely, but said there was "room for manoeuvre" in talks with the Lib Dems and Greens.
And while he has said no matters are "absolutely closed", he wants to "adhere as close to the [SNP] manifesto as possible" on tax, making a deal with the Lib Dems the more likely.
The Lib Dems said they wanted "substantial changes" made, which would "set Scotland on a stronger, more liberal path".
These focus on the party's manifesto pledges around education and mental health. Specific measures include:
Mr Rennie said: "Liberal Democrats will not agree to the draft budget as it stands and will need these substantial changes. If we don't get what the country needs then we will walk away.
"Our plan invests for a step change in mental health and a transformation in education that will help in the road to a liberal Scotland. A properly funded pupil premium and more money for colleges will create that opportunity and boost jobs and the economy.
"New investment in mental health services will boost this Cinderella service and make the whole NHS more sustainable in the future. We have also included support for alcohol and drug services, a higher budget for the police and lower cost transport for the Northern Isles.
"I have had a number of meetings and discussions with the finance secretary so far and I am looking forward to receiving his response to our plan."
Mr Mackay has defended his tax and spending plans in two meetings of the finance committee, where he also took questions from the public over social media.
The committee will submit its report on the budget on Friday 27 January, with the first chamber debate on the budget the following week.
The final vote on the budget will follow a separate vote on Mr Mackay's tax proposals, in the week beginning 20 February.
This is a decent snapshot of what the final budget deal is likely to look like.
Willie Rennie probably won't get absolutely everything he is asking for - one would suspect Derek Mackay is too good a negotiator for that - but this is a far more palatable list of demands for the finance secretary than that put forward by the Greens, who want to see some movement over tax.
While he says nothing is off the table, Mr Mackay isn't going to budge on tax. He sees his current proposals as well-balanced, and endorsed by the electorate last May.
And with a deal with Labour or the Tories more or less dismissed in advance on political grounds, that leaves Mr Rennie as the clear favourite.
He may well have beefed up his demands accordingly - minus any red lines, of course, over tax.
There are plenty of talks still to come, but there is also plenty common ground here. Expect a SNP/Lib Dem coalition to usher an amended budget through come the end of February.
The Liberal Democrats have set out funding for education, mental health and transport links as their demands for backing the Scottish budget.