The Government lost four Dáil votes on Thursday.
The votes covered motions on securing a special status for the North post-Brexit and on the North-South electricity interconnector.
The Coalition lost in three votes on its approach to Brexit.
It lost the votes on a private members’ motion submitted by Sinn Féin, which called for the Government to negotiate for the North to retain a special status within the EU when Britain leaves the bloc.
The Sinn Féin motion also called for quarterly reports to the Dáil by the Government on Brexit negotiations and for all of Ireland to remain within the EU after Brexit.
During a Dáil debate on Wednesday, Minister for Foreign Affairs Charlie Flanagan had warned against Ireland seeking special status within the EU because it would "risk undermining the Government's efforts to specifically address and mitigate the very real impacts facing our island" after Brexit.
The Government submitted an Amendment to Sinn Féin’s motion in support of this approach.
This Amendment was rejected by 59 votes to 84 in a vote on Thursday, although it was supported by Independents Noel Grealish, Michael Lowry and Michael Harty.
However, the Dáil accepted Mr Donnelly’s Amendment, which added detail to Sinn Féin’s motion, by 77 votes to 65.
The Anti-Austerity Alliance-People Before Profit supported the Government, as did the same three Independents.
The composite Sinn Féin/Fianna Fáil motion was then accepted by 77 to 61 votes.
North-South interconnector
The Government was also defeated by 76 votes to 60 on a Fianna Fáil private members’ motion on the controversial North-South interconnector.
The project has been granted planning permission to construct 299 pylons across counties Meath, Cavan and Monaghan, to huge local opposition.
The Fianna Fáil motion called on the Government to commission an independent report to examine the feasibility and cost of putting the interconnector underground and to ensure no further work is done on the interconnector until that analysis and a full community consultation are completed.
The Government’s similar but differently-worded Amendment called for the concerns of Cavan, Meath and Monaghan communities to be taken on board and for the publication of an independent analysis of the relative cost differences of underground and overground systems.
The Green Party supported the Government on the motion.